Papers On Sturm-Liouville Theory

Transcription

1 Papers On Sturm-Liouville Theory References [1] C. Fulton, Parametrizations of Titchmarsh s m()- Functions in the limit circle case, Trans. Amer. Math. Soc. 229, (1977), [2] C. Fulton, Parametrizations of Titchmarsh s m()- Functions in the limit circle case, D.Sc. Diss., Rheinisch-Westfälishe Technische Hochshcule Aachen, Aachen, Germany, [3] C. Fulton, Two-Point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. Roy. Soc. Edin. 77A, (1977), [4] C. Fulton, Singular eigenvalue problems with eigenvalue parameter contained in the boundary conditions. Proc. Roy. Soc. Edin. Sect. 87A, (1980/81), no. 1-2, [5] C. Fulton, Asymptotics of the m-coe cient for eigenvalue problems with eigenparameter in the boundary conditions, Bull. London Math. Soc. 13(6), (1981), [6] C. Fulton, Expansions in Legendre Functions, Quart. J. Math., Oxford 33(2), (1982), [7] C. Fulton, An integral equation iterative scheme for asymptotic expansions of spectral quantities of regular Sturm-Liouville problems, Jour. Integral Equas. 4, (1982), [8] F. V. Atkinson and C. Fulton, Some limit circle eigenvalue problems and asymptotic formulae for eigenvalues. Proc. of 7 th Dundee Conference, Scotland, March 29-April 2, Lecture Notes in Mathematics 964, Springer (1982), pp [9] C. Fulton, Some open problems on asymptotics of m-coe ents, Proc. of Conference on Spectral Theory of Di erential Operators, Birmingham, Alabama, March 26-28, (1981); I. Knowles and R. Lewis, Spectral Theory of Di erential Operators, North Holland Mathematics Studies 55, North Holland (1981), [10] F. V. Atkinson and C. Fulton, Asymptotic formulae for eigenvalues of limit circle problems on a half line. Ann. Mat. Pura Appl. 135(4), (1983), [11] F. V. Atkinson and C.Fulton, Asymptotics of Sturm-Liouville eigenvalues for problems on a nite interval with one limit-circle singularity., I. Proc. Roy. Soc. Edin. 99A (1-2), (1984),

2 [12] A. Krall and C. Fulton, Self-Adjoint 4 th order boundary value problem, Proc. of Symposium on Ordinary Di erential Equations and Operators, Dundee, Scottland, March-July, 1982, Lecture Notes in Mathematics 1032, Springer (1983), [13] C. Fulton, The Bessel-Squared equation in the Lim-2, Lim-3, Lim-4 cases, Quart. Jour. Math. Oxford 40 (2), (1989), [14] C. Fulton and S. Pruess, Eigenvalue and Eigenfunction asymptotics for regular Sturm-Liouville problems, J. Math. Anal. Appl. 188 (1), (1994), [15] C. Fulton, L. Wu and S. Pruess, A Sturm separation theorem for a linear 2n th order self-adjoint di erential equation, J. Appl. Math. Stochastic Anal. 8 (1), (1995), [16] C. Fulton, S. Pruess and L. Wu, Equivalence of various characterizations of the oscillatory/nonoscillatory classi cations for singular endpoints of fourth order self-adjoint di erential equations, World Congress of Nonlinear Analysts 92 Vol. I IV, Walter de Gruyter, Berlin, (1996), [17] C. Fulton, On generating theorems and conjectures in spectral theory with computer assistance. Spectral theory and computational methods of Sturm-Liouville problems, Lecture Notes in Pure and Appl. Math. 191, (eds. D. Hinton and P. W. Schaefer), Marcel Dekker, New York, (1997), [18] F. Atkinson and C. Fulton, Asymptotics of the Titchmarsh-Weyl m-coe cient for non-integrable potentials, Proc. Roy. Soc. Edin. 129A (4), (1999), [19] C. Fulton, Titchmarsh-Weyl m-functions for second-order Sturm-Liouville problems with two singular endpoints, Math. Nachr. 281 (10), (2008), [20] C. Fulton and H. Langer, Sturm-Liouville operators with singularities and Generalized Nevenlinna functions, Complex Analysis Operator Theory, DOI /s , published online, July 14, 2009 at springer.com. [21] C. Knoll and C. Fulton, Using a computer algebra system to simplify expressions for Titchmarsh-Weyl m-functions associated with the Hydrogen Atom on the half line, Florida Institute of Technology Research Report, (Available as arxiv ). Papers in Computational Spectral Theory and Software [22] C. Fulton, and S. Pruess, Numerical methods for a singular eigenvalue problem with eigenparameter in the boundary conditions, J. Math. Anal. Appl. 71 (2), (1979),

3 [23] C. Fulton and S. Pruess, A User s Guide to Subroutine SPDNSF, Proc. of the Focused Reseach Program on Spectral Theory and Boundary Value Problems, Argonne National Laboratory Technical Report ANL-87-26, Vol 3, (1989), [24] C. Fulton and S. Pruess, Mathematical Software for Sturm-Liouville Problems, ACM Trans. on Math. Software 19, (1993), [25] S. Pruess, C. Fulton and Y. Xie, An asymptotic numerical method for a class of singular Sturm-Liouville problems, SIAM J. Numer. Anal. 32 (5), (1995), [26] C. Fulton, S. Pruess and Y. Xie, Performance of the Sturm-Liouville Software Package SLEDGE, Technical Report MCS-91-19, Colorado School of Mines, Department of Mathematical and Computer Sciences, December [27] S. Pruess and C. Fulton, Numerical Approximation of Singular Spectral Functions arising from the Fourier-Jacobi Problem on the half line with continuous spectra, Lecture Notes in Pure and Applied Mathematics 157, Fourier Analysis: Analytic and Geometric Aspects, W. Bray, P. Milojevic and C. Stanojevic, Marcel Dekker, (1994), [28] M. S. P. Eastham, S. Pruess and C. Fulton, Using the SLEDGE package on Sturm-Liouville problems having nonempty essential spectrum, ACM Trans. on Math. Software 22 (4), (1996), [29] C. Fulton, S. Pruess and W. Shoa, Parallel Computation of Sturm-Liouville Spectral Density Functions, Parallel Algorithms and Applications 4, (1994), [30] S. Pruess and C. Fulton, Error analysis in the approximation of Sturm-Liouville spectral density functions, J. Math. Anal. Appl. 203 (2), (1996), [31] C. Fulton and S. Pruess, The computation of spectral density functions for singular Sturm-Liouville problems involving simple continuous spectra, ACM Trans. Math. Software 34 (1), (1998), [32] C. Fulton, S. Pruess and Y. Xie, The automatic Classi cation of Sturm-Liouville Problems, Journal of Applied Mathematics and Computation, Accepted for publication. [33] C. Fulton, D. Pearson and S. Pruess, Computing the Spectral Function for singular Sturm-Liouville Problems, J. Comput. Appl. Math. 176 (1) (2005), [34] C. Fulton, D. Pearson and S. Pruess, New characterizations of spectral density functions for singular Sturm-Liouville problems, J. Comput. Appl. Math. 212 (2), (2008),

4 [35] C. Fulton, D. Pearson and S. Pruess, E cient calculation of spectral density functions for speci c classes of singular Sturm-Liouville problems, J. Comput. Appl. Math. 212 (2), (2008), [36] C. Fulton, D. Pearson and S. Pruess, Titchmarsh-Weyl theory for tridiagonal Jacobi matrices and computation of their spectral functions, Chap. 15, , in Advances in Mathematical Problems in Engineering Aerospace and Sciences, ed S. Sivasundaram, Cambridge Scienti c Publishers, Ltd. December Papers in Numerical Analysis and Numerical Linear Algebra [37] C. Fulton and M. Chinichiaan, Software for closed-form solutions of linear timeinvariant di erential systems, IEEE Circuits and Devices Magazine 2 (3), (1986), [38] D. Fausett and C. Fulton, Large Least Square problems involving Kronecker products, SIAM J. Matrix Anal. Appl. 15 (1), (1994), [39] D. Fauset, C. Fulton and H. Hashish, Parallel QR method for large least squares problems involving Kronecker products, Internat. J. Appl. Sci. Comput. 2(3), (1996), [40] C. Fulton, D. Fauset and H. Hashish, Improved Parallel QR method for large least squares problems involving Kronecker products, Proc. of 14th. IMACS World Congress on Computation and Applied Mathematics, July 11-15, 1994, Atlanta, GA. [41] C. Fulton, D. Fauset and H. Hashish, Parallel QR method for large least squares problems involving Kronecker products, Intl. Jour. Appl. Sci. Comput. 2 (3), (1996), [42] C. Fulton, D. Fauset and H. Hashish, Improved Parallel QR method for large least squares problems involving Kronecker products, Jour. of Comput. Appl. Math. 78, (1997), [43] C. Fulton and L. Wu, Parallel Computation of large least squares problems involving Kronecker products on the Connection Machine 5, Proc. of the 8th International Conference on Parallel and Distributed Computing Systems, Orlando, Sept , 1995, [44] C. Fulton and L. Wu, Parallel Algorithms for large least squares problems involving Kronecker Products, Nonlinear Analysis, Theory, Methods and Applications 30 (8), (1997),

5 [45] C. Fulton and L. Wu, An Accurate Method for large least squares problems involving Kronecker products on the Connection Machine 5, Proc. of 8th. SIAM Conference on Parallel Processing for Scienti c Computing, March 14-17, 1997 (Available from SIAM on CD-ROM). [46] C. Fulton, G. Howell and D. Richardson, et. al., Some Issues in E cient Implementation of a Vector Based Model for Document Retrieval, Proc. of International Symposium on Information Systems and Engineering, eds. W. Samari, N. Melab, L. Yetongnon, Csrea Press, (2002), [47] C. Fulton, G. Howell, J. Demmel, S. Hammarling and K. Marmol, Cache-E cient Bidiagonalization using BLAS 2.5 Operators, ACM Trans. on Math. Softw. 34 (3), (2008),