Selected Topics in Integral Geometry
|
|
- Marylou Edwards
- 5 years ago
- Views:
Transcription
1 Translations of MATHEMATICAL MONOGRAPHS Volume 220 Selected Topics in Integral Geometry I. M. Gelfand S. G. Gindikin M. I. Graev American Mathematical Society 'I Providence, Rhode Island
2 Contents Preface to the English Edition Preface Chapter 1. Radon Transform 1 1. Radon transform on the plane Radon transform on the Euclidean plane Inversion formula Remarks Radon transform on the affine plane Relation to the Fourier transform and another proof of the inversion formula 5 2. Radon transform in three-dimensional space Radon transform in Euclidean space Radon transform in the affine space Radon transform for a space of arbitrary dimension Wave equation and the Huygens principle Two-dimensional case Three-dimensional case Cavalieri's conditions and Paley-Wiener theorems for the Radon transform Cavalieri's conditions for rapidly decreasing functions Paley-Wiener theorem for the space 5(M 2 ) Paley-Wiener theorem for the space X>(M 2 ) of compactly supported infinitely differentiable functions Inversion of the Radon transform of a function / 2?(M 2 ) using the moments Reconstruction of unknown directions from known values of 72./ Poisson formula for the Radon transform, and the discrete Radon transform Poisson formula for the Radon transform on a plane Discrete Radon transform; relation to the Fourier series Problem of integral geometry on the torus Minkowski-Funk transform Radon transform of differential forms Radon transform of 1-forms on the plane Radon transform of 2-forms on the plane Radon transform of 2-forms in three-dimensional space Radon transform of 3-forms in three-dimensional space Radon transform for the projective plane and projective space 30 xi xiii
3 vi 8.1. Spaces P 3 and (P 3 )' Radon transform for P Relation to the affine Radon transform for M 3 and to the Minkowski-Funk transform for the three-dimensional sphere Inversion formula for the Radon transform on P On the inversion formulas for the affine Radon transform on R 3 and the Minkowski-Funk transform for S Description of the image of the Radon transform for P Radon transform for the projective plane P Radon transform for the projective space of an arbitrary dimension Radon transform on the complex affine space Definition of the Radon transform Relation to the Fourier transform Inversion formula for the Radon transform Case n = Relation to Paley-Wiener theorems for the affine Radon transform in M 2 and R 3 40 Chapter 2. John Transform John transform in the real affine space John transform in R John transform and the Gauss hypergeometric function Theorem on the image of the operator J Space S(H') Description of the image of (]R 3 ) in the space S(H') Proof of Theorem 1.1 on the image of the John transform Analogs of the operator K John transform of differential forms on R Definition of the John transform of differential forms John transform of 3-forms on R John transform of 2-forms on R John transform of 1-forms on R John transform in the three-dimensional real projective space Manifold of lines in P John transform in P Relation to the John transform in the affine space Description of the image of the John transform Another way to define the John transform Proof of the theorem on the image of the John transform John transform as an intertwining operator John transform in the complex affine space John transform in C Differential form Kip and the theorem on the image of the John transform Inversion formula Analogs of the operator K Problems of integral geometry for line complexes in C Problem of integral geometry for a complex of lines in C 3 intersecting a curve 71
4 vii 5.2. Definition of admissible line complexes in C Necessary and sufficient conditions for a complex K to be admissible Geometric structure of admissible complexes Description of admissible complexes 76 Chapter 3. Integral Geometry and Harmonic Analysis on the Hyperbolic Plane and in the Hyperbolic Space Elements of hyperbolic planimetry Models of the hyperbolic plane Horocycles Geodesies Horocycle transform Definition of the operator U h Inversion formula Asgeirsson relations Symmetry relation Inversion formula for the horocycle transform in another model of the hyperbolic plane Analog of the Fourier transform on the hyperbolic plane and the relation between this analog and the horocycle transform Fourier transform on R Fourier transform on the hyperbolic plane Relation to the horocycle transform and the inversion formula Symmetry relation Plancherel formula Relation to the representation theory of the group SX(2,R) Integral transform related to lines (geodesies) on the hyperbolic plane Definition and the inversion formula in the Poincare model Relation to the Radon transform on the projective plane Horospherical transform in the three-dimensional hyperbolic space Models of the hyperbolic space Horospheres Horospherical transform Inversion formula Symmetry relation Inversion formula for the horospherical transform in another model of the hyperbolic space Integral transform related to completely geodesic surfaces in Analog of the Fourier transform in the hyperbolic space, and its relation to the horospherical transform Definition of the Fourier transform Inversion formula Symmetry relation and the Plancherel formula Relation to the representation theory for the group SL(2,C) Wave equation for the hyperbolic plane and hyperbolic space, and the Huygens principle Two-dimensional case 106
5 viii 9.2. Three-dimensional case 108 Chapter 4. Integral Geometry and Harmonic Analysis on the Group G = SL(2, C) Geometry on the group G Group G as a homogeneous space Plane sections of the hyperboloid G Manifold of horospheres Embedding the manifold of horospheres H in the projective space Line complex in C 3 associated with the manifold of horospheres Manifold of paraboloids Integral geometry on the group G = SL(2, C) Integral transforms related to the space H of horospheres and the complex of lines K Symmetry relations for the horospherical transform Inversion formula for the integral transform TJ-o related to the line complex K in C Inversion formula for the horospherical transform Inversion formula for the horospherical transform on the hyperbolic space C? Integral transform related to paraboloids on G Harmonic analysis on the group G = SL(2, C) Laplace-Beltrami operator on the group G Horospherical functions on G Fourier transform on G Relation between the Fourier transform on G and the horospherical transform Symmetry relation for the Fourier transform Inversion formula for the Fourier transform Analog of the Plancherel formula Relation between the Fourier transform on G and the representations of the group GxG Relation to the representations of the group G Another version of the Fourier transform on G = SL(2, C) Functions $ x (g;,c) Fourier transform on G Relation between the above two versions of the Fourier transform Symmetry relation Inversion formula and Plancherel formula for the Fourier transform T Relations with representation theory 143 Chapter 5. Integral Geometry on Quadrics Integral transform related to the hyperplane sections of a hyperboloid of two sheets in M. n Definition Admissible submanifolds in the manifold of hyperplane sections of C n Operator K X Local and nonlocal operators K 151
6 ix 1.5. Inversion formula Examples Integral transform related to spheres in Euclidean space E n Definition Operator K X Inversion formula Examples 159 Bibliography 165 Index 167
Modern Geometric Structures and Fields
Modern Geometric Structures and Fields S. P. Novikov I.A.TaJmanov Translated by Dmitry Chibisov Graduate Studies in Mathematics Volume 71 American Mathematical Society Providence, Rhode Island Preface
More informationON RADON TRANSFORMS AND THE KAPPA OPERATOR. François Rouvière (Université de Nice) Bruxelles, November 24, 2006
ON RADON TRANSFORMS AND THE KAPPA OPERATOR François Rouvière (Université de Nice) Bruxelles, November 24, 2006 1. Introduction In 1917 Johann Radon solved the following problem : nd a function f on the
More informationDifferential Geometry, Lie Groups, and Symmetric Spaces
Differential Geometry, Lie Groups, and Symmetric Spaces Sigurdur Helgason Graduate Studies in Mathematics Volume 34 nsffvjl American Mathematical Society l Providence, Rhode Island PREFACE PREFACE TO THE
More informationLectures on the Orbit Method
Lectures on the Orbit Method A. A. Kirillov Graduate Studies in Mathematics Volume 64 American Mathematical Society Providence, Rhode Island Preface Introduction xv xvii Chapter 1. Geometry of Coadjoint
More informationSubmanifolds of. Total Mean Curvature and. Finite Type. Bang-Yen Chen. Series in Pure Mathematics Volume. Second Edition.
le 27 AIPEI CHENNAI TAIPEI - Series in Pure Mathematics Volume 27 Total Mean Curvature and Submanifolds of Finite Type Second Edition Bang-Yen Chen Michigan State University, USA World Scientific NEW JERSEY
More informationContents. Preface. Notation
Contents Preface Notation xi xv 1 The fractional Laplacian in one dimension 1 1.1 Random walkers with constant steps.............. 1 1.1.1 Particle number density distribution.......... 2 1.1.2 Numerical
More informationMathematics for Engineers and Scientists
Mathematics for Engineers and Scientists Fourth edition ALAN JEFFREY University of Newcastle-upon-Tyne B CHAPMAN & HALL University and Professional Division London New York Tokyo Melbourne Madras Contents
More informationNew Perspectives. Functional Inequalities: and New Applications. Nassif Ghoussoub Amir Moradifam. Monographs. Surveys and
Mathematical Surveys and Monographs Volume 187 Functional Inequalities: New Perspectives and New Applications Nassif Ghoussoub Amir Moradifam American Mathematical Society Providence, Rhode Island Contents
More informationTHEORY OF GROUP REPRESENTATIONS AND APPLICATIONS
THEORY OF GROUP REPRESENTATIONS AND APPLICATIONS ASIM 0. BARUT Institute for Theoretical Physics, University of Colorado, Boulder, Colo., U.S.A. RYSZARD RATJZKA Institute for Nuclear Research, Warszawa,
More informationHypersingular Integrals and Their Applications
Hypersingular Integrals and Their Applications Stefan G. Samko Rostov State University, Russia and University ofalgarve, Portugal London and New York Contents Preface xv Notation 1 Part 1. Hypersingular
More informationContents. 1 Basic Equations 1. Acknowledgment. 1.1 The Maxwell Equations Constitutive Relations 11
Preface Foreword Acknowledgment xvi xviii xix 1 Basic Equations 1 1.1 The Maxwell Equations 1 1.1.1 Boundary Conditions at Interfaces 4 1.1.2 Energy Conservation and Poynting s Theorem 9 1.2 Constitutive
More informationPatrick Iglesias-Zemmour
Mathematical Surveys and Monographs Volume 185 Diffeology Patrick Iglesias-Zemmour American Mathematical Society Contents Preface xvii Chapter 1. Diffeology and Diffeological Spaces 1 Linguistic Preliminaries
More informationTheta Constants, Riemann Surfaces and the Modular Group
Theta Constants, Riemann Surfaces and the Modular Group An Introduction with Applications to Uniformization Theorems, Partition Identities and Combinatorial Number Theory Hershel M. Farkas Irwin Kra Graduate
More informationLebesgue Integration on Euclidean Space
Lebesgue Integration on Euclidean Space Frank Jones Department of Mathematics Rice University Houston, Texas Jones and Bartlett Publishers Boston London Preface Bibliography Acknowledgments ix xi xiii
More informationTheorem 2. Let n 0 3 be a given integer. is rigid in the sense of Guillemin, so are all the spaces ḠR n,n, with n n 0.
This monograph is motivated by a fundamental rigidity problem in Riemannian geometry: determine whether the metric of a given Riemannian symmetric space of compact type can be characterized by means of
More informationKlaus Janich. Vector Analysis. Translated by Leslie Kay. With 108 Illustrations. Springer
Klaus Janich Vector Analysis Translated by Leslie Kay With 108 Illustrations Springer Preface to the English Edition Preface to the First German Edition Differentiable Manifolds 1 1.1 The Concept of a
More informationSystolic Geometry and Topology
Mathematical Surveys and Monographs Volume 137 Systolic Geometry and Topology Mikhail G. Katz With an Appendix by Jake P. Solomon American Mathematical Society Contents Preface Acknowledgments xi xiii
More informationMetric Structures for Riemannian and Non-Riemannian Spaces
Misha Gromov with Appendices by M. Katz, P. Pansu, and S. Semmes Metric Structures for Riemannian and Non-Riemannian Spaces Based on Structures Metriques des Varietes Riemanniennes Edited by J. LaFontaine
More information612 CLASS LECTURE: HYPERBOLIC GEOMETRY
612 CLASS LECTURE: HYPERBOLIC GEOMETRY JOSHUA P. BOWMAN 1. Conformal metrics As a vector space, C has a canonical norm, the same as the standard R 2 norm. Denote this dz one should think of dz as the identity
More informationAlgebraic Curves and Riemann Surfaces
Algebraic Curves and Riemann Surfaces Rick Miranda Graduate Studies in Mathematics Volume 5 If American Mathematical Society Contents Preface xix Chapter I. Riemann Surfaces: Basic Definitions 1 1. Complex
More informationYAO LIU. f(x t) + f(x + t)
DUNKL WAVE EQUATION & REPRESENTATION THEORY OF SL() YAO LIU The classical wave equation u tt = u in n + 1 dimensions, and its various modifications, have been studied for centuries, and one of the most
More informationGeneralized Functions Theory and Technique Second Edition
Ram P. Kanwal Generalized Functions Theory and Technique Second Edition Birkhauser Boston Basel Berlin Contents Preface to the Second Edition x Chapter 1. The Dirac Delta Function and Delta Sequences 1
More informationIntroduction to the Mathematics of Medical Imaging
Introduction to the Mathematics of Medical Imaging Second Edition Charles L. Epstein University of Pennsylvania Philadelphia, Pennsylvania EiaJTL Society for Industrial and Applied Mathematics Philadelphia
More informationCOPYRIGHTED MATERIAL CONTENTS. Preface Preface to the First Edition
Preface Preface to the First Edition xi xiii 1 Basic Probability Theory 1 1.1 Introduction 1 1.2 Sample Spaces and Events 3 1.3 The Axioms of Probability 7 1.4 Finite Sample Spaces and Combinatorics 15
More informationENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS. Special Functions GEORGE E. ANDREWS RICHARD ASKEY RANJAN ROY CAMBRIDGE UNIVERSITY PRESS
ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS Special Functions GEORGE E. ANDREWS RICHARD ASKEY RANJAN ROY CAMBRIDGE UNIVERSITY PRESS Preface page xiii 1 The Gamma and Beta Functions 1 1.1 The Gamma
More informationAPPLIED PARTIAL DIFFERENTIAL EQUATIONS
APPLIED PARTIAL DIFFERENTIAL EQUATIONS AN I N T R O D U C T I O N ALAN JEFFREY University of Newcastle-upon-Tyne ACADEMIC PRESS An imprint of Elsevier Science Amsterdam Boston London New York Oxford Paris
More informationAnalytic Number Theory
American Mathematical Society Colloquium Publications Volume 53 Analytic Number Theory Henryk Iwaniec Emmanuel Kowalski American Mathematical Society Providence, Rhode Island Contents Preface xi Introduction
More informationMATH 2083 FINAL EXAM REVIEW The final exam will be on Wednesday, May 4 from 10:00am-12:00pm.
MATH 2083 FINAL EXAM REVIEW The final exam will be on Wednesday, May 4 from 10:00am-12:00pm. Bring a calculator and something to write with. Also, you will be allowed to bring in one 8.5 11 sheet of paper
More informationMostow Rigidity. W. Dison June 17, (a) semi-simple Lie groups with trivial centre and no compact factors and
Mostow Rigidity W. Dison June 17, 2005 0 Introduction Lie Groups and Symmetric Spaces We will be concerned with (a) semi-simple Lie groups with trivial centre and no compact factors and (b) simply connected,
More informationRepresentation of Lie Groups and Special Functions
Representation of Lie Groups and Special Functions Recent Advances by N. Ja. Vilenkint formerly of The Correspondence Pedagogical Institute, Moscow, Russia and A.U. Klimyk Institute for Theoretical Physics,
More informationMultiplicity One Theorem in the Orbit Method
Amer. Math. Soc. Transl. (2) Vol. 00, XXXX Multiplicity One Theorem in the Orbit Method Toshiyuki Kobayashi and Salma Nasrin In memory of Professor F. Karpelevič Abstract. Let G H be Lie groups, g h their
More information762 BOOK REVIEWS VICTOR GULLLEMLN
758 BOOK REVIEWS BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 3, Number 1, July 1980 1980 American Mathematical Society 0002-9904/80/0000-0314/$02.25 Generalized functions: Volume
More informationThe Mathematics of Minkowski Space-Time
Frontiers in Mathematics The Mathematics of Minkowski Space-Time With an Introduction to Commutative Hypercomplex Numbers Bearbeitet von Francesco Catoni, Dino Boccaletti, Roberto Cannata, Vincenzo Catoni,
More informationThe Fractional Fourier Transform with Applications in Optics and Signal Processing
* The Fractional Fourier Transform with Applications in Optics and Signal Processing Haldun M. Ozaktas Bilkent University, Ankara, Turkey Zeev Zalevsky Tel Aviv University, Tel Aviv, Israel M. Alper Kutay
More informationProjective geometry and spacetime structure. David Delphenich Bethany College Lindsborg, KS USA
Projective geometry and spacetime structure David Delphenich Bethany College Lindsborg, KS USA delphenichd@bethanylb.edu Affine geometry In affine geometry the basic objects are points in a space A n on
More informationThe Erwin Schrodinger International Boltzmanngasse 9. Institute for Mathematical Physics A-1090 Wien, Austria
ESI The Erwin Schrodinger International Boltzmanngasse 9 Institute for Mathematical Physics A-1090 Wien, Austria Real Integral Geometry and Complex Analysis Simon Gindikin Vienna, Preprint ESI 381 (1996)
More informationGROUP THEORY IN PHYSICS
GROUP THEORY IN PHYSICS Wu-Ki Tung World Scientific Philadelphia Singapore CONTENTS CHAPTER 1 CHAPTER 2 CHAPTER 3 CHAPTER 4 PREFACE INTRODUCTION 1.1 Particle on a One-Dimensional Lattice 1.2 Representations
More informationIntroduction to Quadratic Forms over Fields
Introduction to Quadratic Forms over Fields T.Y. Lam Graduate Studies in Mathematics Volume 67.. American Mathematical Society 1 " " M Providence, Rhode Island Preface xi ; Notes to the Reader xvii Partial
More informationSPECIAL FUNCTIONS OF MATHEMATICS FOR ENGINEERS
SPECIAL FUNCTIONS OF MATHEMATICS FOR ENGINEERS Second Edition LARRY C. ANDREWS OXFORD UNIVERSITY PRESS OXFORD TOKYO MELBOURNE SPIE OPTICAL ENGINEERING PRESS A Publication of SPIE The International Society
More informationTHE SELBERG TRACE FORMULA OF COMPACT RIEMANN SURFACES
THE SELBERG TRACE FORMULA OF COMPACT RIEMANN SURFACES IGOR PROKHORENKOV 1. Introduction to the Selberg Trace Formula This is a talk about the paper H. P. McKean: Selberg s Trace Formula as applied to a
More informationSTATISTICS; An Introductory Analysis. 2nd hidition TARO YAMANE NEW YORK UNIVERSITY A HARPER INTERNATIONAL EDITION
2nd hidition TARO YAMANE NEW YORK UNIVERSITY STATISTICS; An Introductory Analysis A HARPER INTERNATIONAL EDITION jointly published by HARPER & ROW, NEW YORK, EVANSTON & LONDON AND JOHN WEATHERHILL, INC.,
More informationWilliam P. Thurston. The Geometry and Topology of Three-Manifolds
William P. Thurston The Geometry and Topology of Three-Manifolds Electronic version 1.1 - March 00 http://www.msri.org/publications/books/gt3m/ This is an electronic edition of the 1980 notes distributed
More informationANALYTIC DEFINITIONS FOR HYPERBOLIC OBJECTS. 0. Introduction
Trends in Mathematics Information Center for Mathematical Sciences Volume 5, Number 1,June 00, Pages 11 15 ANALYTIC DEFINITIONS FOR HYPERBOLIC OBJECTS YUNHI CHO AND HYUK KIM Abstract We can extend the
More informationSpherical Inversion on SL n (R)
Jay Jorgenson Serge Lang Spherical Inversion on SL n (R) Springer Contents Acknowledgments Overview Table of the Decompositions ix xi xvii CHAPTER I Iwasawa Decomposition and Positivity 1 1. The Iwasawa
More informationIndex. Bertrand mate, 89 bijection, 48 bitangent, 69 Bolyai, 339 Bonnet s Formula, 283 bounded, 48
Index acceleration, 14, 76, 355 centripetal, 27 tangential, 27 algebraic geometry, vii analytic, 44 angle at a corner, 21 on a regular surface, 170 angle excess, 337 angle of parallelism, 344 angular velocity,
More informationHyperbolic Conformal Geometry with Clifford Algebra 1)
MM Research Preprints, 72 83 No. 18, Dec. 1999. Beijing Hyperbolic Conformal Geometry with Clifford Algebra 1) Hongbo Li Abstract. In this paper we study hyperbolic conformal geometry following a Clifford
More informationElementary Applications of Probability Theory
Elementary Applications of Probability Theory With an introduction to stochastic differential equations Second edition Henry C. Tuckwell Senior Research Fellow Stochastic Analysis Group of the Centre for
More informationInternational Series in Analysis
International Series in Analysis A Textbook in Modern Analysis Editor Shing-Tung Yau IP International Press Claus Gerhardt Analysis II Claus Gerhardt Ruprecht-Karls-Universität Institut für Angewandte
More informationChapter 13: Vectors and the Geometry of Space
Chapter 13: Vectors and the Geometry of Space 13.1 3-Dimensional Coordinate System 13.2 Vectors 13.3 The Dot Product 13.4 The Cross Product 13.5 Equations of Lines and Planes 13.6 Cylinders and Quadratic
More informationChapter 13: Vectors and the Geometry of Space
Chapter 13: Vectors and the Geometry of Space 13.1 3-Dimensional Coordinate System 13.2 Vectors 13.3 The Dot Product 13.4 The Cross Product 13.5 Equations of Lines and Planes 13.6 Cylinders and Quadratic
More informationDispersive Equations and Nonlinear Waves
Herbert Koch Daniel Tataru Monica Vi an Dispersive Equations and Nonlinear Waves Generalized Korteweg-de Vries, Nonlinear Schrodinger, Wave and Schrodinger Maps ^ Birkhauser Contents Preface xi Nonlinear
More informationMath 302 Outcome Statements Winter 2013
Math 302 Outcome Statements Winter 2013 1 Rectangular Space Coordinates; Vectors in the Three-Dimensional Space (a) Cartesian coordinates of a point (b) sphere (c) symmetry about a point, a line, and a
More informationRepresentation of Lie Groups and Special Functions
Representation of Lie Groups and Special Functions Mathematics and Its Applications Managing Editor: M. HAZEWINKEL Centre for Mathematics and Computer Science. Amsterdam. The Netherlands Volume 316 Representation
More informationWe wish the reader success in future encounters with the concepts of linear algebra.
Afterword Our path through linear algebra has emphasized spaces of vectors in dimension 2, 3, and 4 as a means of introducing concepts which go forward to IRn for arbitrary n. But linear algebra does not
More informationCONTENTS. Preface Preliminaries 1
Preface xi Preliminaries 1 1 TOOLS FOR ANALYSIS 5 1.1 The Completeness Axiom and Some of Its Consequences 5 1.2 The Distribution of the Integers and the Rational Numbers 12 1.3 Inequalities and Identities
More informationTHE PRINCIPLES AND PRACTICE OF STATISTICS IN BIOLOGICAL RESEARCH. Robert R. SOKAL and F. James ROHLF. State University of New York at Stony Brook
BIOMETRY THE PRINCIPLES AND PRACTICE OF STATISTICS IN BIOLOGICAL RESEARCH THIRD E D I T I O N Robert R. SOKAL and F. James ROHLF State University of New York at Stony Brook W. H. FREEMAN AND COMPANY New
More informationNatural Boundary Integral Method and Its Applications
Natural Boundary Integral Method and Its Applications By De-hao Yu State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing
More informationSPHERICAL NEAR-FIELD ANTENNA MEASUREMENTS
SPHERICAL NEAR-FIELD ANTENNA MEASUREMENTS Edited by J.E.Hansen Peter Peregrinus Ltd. on behalf of the Institution of Electrical Engineers Contents Contributing authors listed Preface v xiii 1 Introduction
More informationSIGNALS AND SYSTEMS I. RAVI KUMAR
Signals and Systems SIGNALS AND SYSTEMS I. RAVI KUMAR Head Department of Electronics and Communication Engineering Sree Visvesvaraya Institute of Technology and Science Mahabubnagar, Andhra Pradesh New
More informationADVANCED ENGINEERING MATHEMATICS
ADVANCED ENGINEERING MATHEMATICS DENNIS G. ZILL Loyola Marymount University MICHAEL R. CULLEN Loyola Marymount University PWS-KENT O I^7 3 PUBLISHING COMPANY E 9 U Boston CONTENTS Preface xiii Parti ORDINARY
More informationLinear Differential Transformations of the Second Order
Linear Differential Transformations of the Second Order In: Otakar Borůvka (author); Felix M. Arscott (translator): Linear Differential Transformations of the Second Order. (English). London: The English
More informationMETHODS FOR SOLVING MATHEMATICAL PHYSICS PROBLEMS
METHODS FOR SOLVING MATHEMATICAL PHYSICS PROBLEMS V.I. Agoshkov, P.B. Dubovski, V.P. Shutyaev CAMBRIDGE INTERNATIONAL SCIENCE PUBLISHING Contents PREFACE 1. MAIN PROBLEMS OF MATHEMATICAL PHYSICS 1 Main
More informationVertex Algebras and Algebraic Curves
Mathematical Surveys and Monographs Volume 88 Vertex Algebras and Algebraic Curves Edward Frenkei David Ben-Zvi American Mathematical Society Contents Preface xi Introduction 1 Chapter 1. Definition of
More informationDifferential Equations
Differential Equations Theory, Technique, and Practice George F. Simmons and Steven G. Krantz Higher Education Boston Burr Ridge, IL Dubuque, IA Madison, Wl New York San Francisco St. Louis Bangkok Bogota
More informationHolographic Special Relativity:
Holographic Special Relativity: Observer Space from Conformal Geometry Derek K. Wise University of Erlangen Based on 1305.3258 International Loop Quantum Gravity Seminar 15 October 2013 1 Holographic special
More informationApplied Asymptotic Analysis
Applied Asymptotic Analysis Peter D. Miller Graduate Studies in Mathematics Volume 75 American Mathematical Society Providence, Rhode Island Preface xiii Part 1. Fundamentals Chapter 0. Themes of Asymptotic
More informationContents. 1 Preliminaries 3. Martingales
Table of Preface PART I THE FUNDAMENTAL PRINCIPLES page xv 1 Preliminaries 3 2 Martingales 9 2.1 Martingales and examples 9 2.2 Stopping times 12 2.3 The maximum inequality 13 2.4 Doob s inequality 14
More informationUNIVERSITY OF DUBLIN
UNIVERSITY OF DUBLIN TRINITY COLLEGE JS & SS Mathematics SS Theoretical Physics SS TSM Mathematics Faculty of Engineering, Mathematics and Science school of mathematics Trinity Term 2015 Module MA3429
More informationMECH 576 Geometry in Mechanics September 16, 2009 Using Line Geometry
MECH 576 Geometry in Mechanics September 16, 2009 Using Line Geometry 1 Deriving Equations in Line Coordinates Four exercises in deriving fundamental geometric equations with line coordinates will be conducted.
More informationSpecial Functions of Mathematical Physics
Arnold F. Nikiforov Vasilii B. Uvarov Special Functions of Mathematical Physics A Unified Introduction with Applications Translated from the Russian by Ralph P. Boas 1988 Birkhäuser Basel Boston Table
More informationHuygens principle and a Paley Wiener type Theorem on Damek Ricci spaces
Annales mathématiques Blaise Pascal Working version March 29, 2010 Huygens principle and a Paley Wiener type Theorem on Damek Ricci spaces Francesca Astengo Bianca Di Blasio Abstract. We prove that Huygens
More informationNUMERICAL COMPUTATION IN SCIENCE AND ENGINEERING
NUMERICAL COMPUTATION IN SCIENCE AND ENGINEERING C. Pozrikidis University of California, San Diego New York Oxford OXFORD UNIVERSITY PRESS 1998 CONTENTS Preface ix Pseudocode Language Commands xi 1 Numerical
More informationOrbital and Celestial Mechanics
Orbital and Celestial Mechanics John P. Vinti Edited by Gim J. Der TRW Los Angeles, California Nino L. Bonavito NASA Goddard Space Flight Center Greenbelt, Maryland Volume 177 PROGRESS IN ASTRONAUTICS
More informationThe Mathematics of Computerized Tomography
The Mathematics of Computerized Tomography The Mathematics of Computerized Tomography F. Natterer University of Münster Federal Republic of Germany B. G. TEUBNER Stuttgart @) JOHN WILEY & SONS Chichester.
More informationThe Symmetric Space for SL n (R)
The Symmetric Space for SL n (R) Rich Schwartz November 27, 2013 The purpose of these notes is to discuss the symmetric space X on which SL n (R) acts. Here, as usual, SL n (R) denotes the group of n n
More informationCourse Outline. Date Lecture Topic Reading
Course Outline Date Lecture Topic Reading Graduate Mathematical Physics Tue 24 Aug Linear Algebra: Theory 744 756 Vectors, bases and components Linear maps and dual vectors Inner products and adjoint operators
More informationON Y. NIEVERGELT S INVERSION FORMULA FOR THE RADON TRANSFORM. E. Ournycheva, B. Rubin. Abstract
ON Y. NIEVERGELT S INVERSION FORMULA FOR THE RADON TRANSFORM E. Ournycheva, B. Rubin Abstract In 986 Y. Nievergelt suggested a simple formula which allows to reconstruct a continuous compactly supported
More informationContents Introduction and Review Boundary Behavior The Heisenberg Group Analysis on the Heisenberg Group
Contents 1 Introduction and Review... 1 1.1 Harmonic Analysis on the Disc... 1 1.1.1 The Boundary Behavior of Holomorphic Functions... 4 Exercises... 15 2 Boundary Behavior... 19 2.1 The Modern Era...
More informationTHE FUNDAMENTAL GROUP OF THE DOUBLE OF THE FIGURE-EIGHT KNOT EXTERIOR IS GFERF
THE FUNDAMENTAL GROUP OF THE DOUBLE OF THE FIGURE-EIGHT KNOT EXTERIOR IS GFERF D. D. LONG and A. W. REID Abstract We prove that the fundamental group of the double of the figure-eight knot exterior admits
More informationChapter 3. Riemannian Manifolds - I. The subject of this thesis is to extend the combinatorial curve reconstruction approach to curves
Chapter 3 Riemannian Manifolds - I The subject of this thesis is to extend the combinatorial curve reconstruction approach to curves embedded in Riemannian manifolds. A Riemannian manifold is an abstraction
More informationStatistical Methods in HYDROLOGY CHARLES T. HAAN. The Iowa State University Press / Ames
Statistical Methods in HYDROLOGY CHARLES T. HAAN The Iowa State University Press / Ames Univariate BASIC Table of Contents PREFACE xiii ACKNOWLEDGEMENTS xv 1 INTRODUCTION 1 2 PROBABILITY AND PROBABILITY
More informationTHE ENVELOPE OF LINES MEETING A FIXED LINE AND TANGENT TO TWO SPHERES
6 September 2004 THE ENVELOPE OF LINES MEETING A FIXED LINE AND TANGENT TO TWO SPHERES Abstract. We study the set of lines that meet a fixed line and are tangent to two spheres and classify the configurations
More informationHEAT CONDUCTION USING GREEN S FUNCTIONS
HEAT CONDUCTION USING GREEN S FUNCTIONS Preface to the first edition Preface to the second edition Author Biographies Nomenclature TABLE OF CONTENTS FOR SECOND EDITION December 2009 Page viii x xii xiii
More information2 Lie Groups. Contents
2 Lie Groups Contents 2.1 Algebraic Properties 25 2.2 Topological Properties 27 2.3 Unification of Algebra and Topology 29 2.4 Unexpected Simplification 31 2.5 Conclusion 31 2.6 Problems 32 Lie groups
More informationOrdinary Differential Equations and Smooth Dynamical Systems
D.V. Anosov S.Kh. Aranson V.l. Arnold I.U. Bronshtein V.Z. Grines Yu.S. Il'yashenko Ordinary Differential Equations and Smooth Dynamical Systems With 25 Figures Springer I. Ordinary Differential Equations
More informationAND NONLINEAR SCIENCE SERIES. Partial Differential. Equations with MATLAB. Matthew P. Coleman. CRC Press J Taylor & Francis Croup
CHAPMAN & HALL/CRC APPLIED MATHEMATICS AND NONLINEAR SCIENCE SERIES An Introduction to Partial Differential Equations with MATLAB Second Edition Matthew P Coleman Fairfield University Connecticut, USA»C)
More information2 T ρ G and W is the Weyl group. The generalization of this approach developed in 50-s by Harish-Chandra and Godement led to the proof of the uniquene
The theory of group representations is in the center of interest of I. Gelfand. I think that this is related to the nature of this domain which combines analysis, algebra and topology in a very intricate
More informationMalvin H. Kalos, Paula A. Whitlock. Monte Carlo Methods. Second Revised and Enlarged Edition WILEY- BLACKWELL. WILEY-VCH Verlag GmbH & Co.
Malvin H. Kalos, Paula A. Whitlock Monte Carlo Methods Second Revised and Enlarged Edition WILEY- BLACKWELL WILEY-VCH Verlag GmbH & Co. KGaA v I Contents Preface to the Second Edition IX Preface to the
More informationMETHODS OF ENGINEERING MATHEMATICS
METHODS OF ENGINEERING MATHEMATICS Edward J. Hang Kyung K. Choi Department of Mechanical Engineering College of Engineering The University of Iowa Iowa City, Iowa 52242 METHODS OF ENGINEERING MATHEMATICS
More informationBiomedical Signal Processing and Signal Modeling
Biomedical Signal Processing and Signal Modeling Eugene N. Bruce University of Kentucky A Wiley-lnterscience Publication JOHN WILEY & SONS, INC. New York Chichester Weinheim Brisbane Singapore Toronto
More information8.8. Codimension one isoperimetric inequalities Distortion of a subgroup in a group 283
Contents Preface xiii Chapter 1. Geometry and topology 1 1.1. Set-theoretic preliminaries 1 1.1.1. General notation 1 1.1.2. Growth rates of functions 2 1.1.3. Jensen s inequality 3 1.2. Measure and integral
More informationSMOOTH OPTIMAL TRANSPORTATION ON HYPERBOLIC SPACE
SMOOTH OPTIMAL TRANSPORTATION ON HYPERBOLIC SPACE JIAYONG LI A thesis completed in partial fulfilment of the requirement of Master of Science in Mathematics at University of Toronto. Copyright 2009 by
More informationAPPENDICES APPENDIX A. STATISTICAL TABLES AND CHARTS 651 APPENDIX B. BIBLIOGRAPHY 677 APPENDIX C. ANSWERS TO SELECTED EXERCISES 679
APPENDICES APPENDIX A. STATISTICAL TABLES AND CHARTS 1 Table I Summary of Common Probability Distributions 2 Table II Cumulative Standard Normal Distribution Table III Percentage Points, 2 of the Chi-Squared
More informationIt is easy to see that (~])(a, ~) depends only on the plane h itself fined by the choice of the k-frame a.
CROFTON'S FUNCTION AND INVERSION FORMULAS IN REAL INTEGRAL GEOMETRY I. M. Gel'fand and M. I. Graev UDC 519.212.3 0. Introduction This paper is devoted to inversion formulas for an integral transform /~+~q/,
More informationContents. I Basic Methods 13
Preface xiii 1 Introduction 1 I Basic Methods 13 2 Convergent and Divergent Series 15 2.1 Introduction... 15 2.1.1 Power series: First steps... 15 2.1.2 Further practical aspects... 17 2.2 Differential
More informationStochastic Partial Differential Equations with Levy Noise
Stochastic Partial Differential Equations with Levy Noise An Evolution Equation Approach S..PESZAT and J. ZABCZYK Institute of Mathematics, Polish Academy of Sciences' CAMBRIDGE UNIVERSITY PRESS Contents
More informationCohomogeneity one hypersurfaces in CP 2 and CH 2
Cohomogeneity one hypersurfaces in CP 2 and CH 2 Cristina Vidal Castiñeira Universidade de Santiago de Compostela 1st September 2015 XXIV International Fall Workshop on Geometry and Physics, Zaragoza 2015
More informationNote di Matematica ISSN , e-issn Note Mat. 00 (2011) no. 0, 1 35.
Note di Matematica ISSN 1123-2536, e-issn 1590-0932 Note Mat. 00 (2011) no. 0, 1 35. doi:10.1285/i15900932v00n0p1 Premanifolds Ákos G.Horváth Department of Geometry, Mathematical Institute, Budapest University
More informationComplexes of Differential Operators
Complexes of Differential Operators by Nikolai N. Tarkhanov Institute of Physics, Siberian Academy of Sciences, Krasnoyarsk, Russia KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON Contents Preface
More informationControl Theory and its Applications
Control Theory and its Applications E.O. Roxin The University of Rhode Island USA GORDON AND BREACH SCIENCE PUBLISHERS Australia Canada. China France Germany India. Japan Luxembourg Malaysia The Netherlands.
More information