BIBLIOGRAPHY 509. [G79 ]., Estimation du reste dans l étude des valeurs propres des problèmes

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1 BIBLIOGRAPHY [Ag58]. Agmon, The coerciveness problem for integro-differential forms, J. Analyse Math. 6 (1958), [Ag62]., On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems,, Comm. Pure Appl. Math. 15 (1962), [Ag65]., Lectures on Elliptic Boundary Value Problems, Van Nostrand Math. Studies, D. Van Nostrand Publ. Co., Princeton, [Ag65 ]., On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems, Comm. Pure Appl. Math. 18 (1965), [Ag68]., Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators, Arch. Rat. Mech. An. 28 (1968), [A-V63]. M. S. Agranovich and M.I. Vishik, Elliptic problems with a parameter and parabolic problems of a general type, Usp., Mat. Nauk 19 (1963), ; Russ. Math. Surveys 19, [Agr87]. M. S. Agranovich, Some asymptotic formulas for elliptic pseudodifferential operators, Funkt. Analysis Appl. 21 (1987), [An86]. A. S. Andreev, An estimate for the remainder in the asymptotic expansion of the spectrum of pseudodifferential operators of negative order, Funct. Anal. Appl. 20 (1986), [An90]., Asymptotics of the spectrum of compact pseudodifferential operators in a Euclidean domain, Math. USSR Sbornik 65 (1990), [At67]. M. F. Atiyah, K-Theory, Benjamin, Amsterdam, [A-B64]. Atiyah and R. Bott, The index problem for manifolds with boundary, Coll. Differential Analysis, Tata Institute, Bombay, Oxford University Press (1964), [A-B-P73]. M. F. Atiyah, R. Bott and V. K. Patodi, On the heat equation and the index theorem, Inventiones Math. 19 (1973), [A-S68]. M. F. Atiyah and I. M. Singer, The index of elliptic operators, Ann. of Math. 87 (1968), [Bar94]. M. Baranowski, On pseudodifferential boundary problems, work in progress, personal communication in [Be67]. R. Beals, Classes of compact operators and eigenvalue distribution for elliptic operators, Am. J. Math. 89 (1967), [Be70]., Asymptotic behavior of the Green s function and spectral function of an elliptic operator, J. Functional Analysis 5 (1970), [Bi56]. M. S. Birman, On the theory of self-adjoint extensions of positive definite operators, Mat. Sb. 38: 90 (1956), , (Russian). [B-S77]. M. S. Birman and M. Z. Solomiak, Estimates of singular numbers of integral operators, Russian Math. Surveys 32 (1977),

2 BIBLIOGRAPHY 507 [B-S77 ]., Asymptotics of the spectra of pseudodifferential operators with anisotropic-homogeneous symbols, Vestnik Leningrad Univ. 13 (1977), [B-S77 ]., Asymptotic behavior of the spectrum of differential equations, Itogi Nauk. Tekh., Mat. An. 14 (1977), 5 58; J. Soviet Math. 12 (1979), [B-C-P68]. J. M. Bony, P. Courrège and P. Priouret, Semi-groupes de Feller sur une variété à bord compacte et problèmes aux limites intégro-différentiels du second ordre donnant lieu au principe du maximum, Ann. Inst. Fourier (Grenoble) 18 (1968), [BM66]. L. Boutet de Monvel, Comportement d un opérateur pseudo-différentiel sur une variéte à bord, I-II, J. d Analyse Fonct. 17 (1966), [BM69]., Opérateurs pseudo-differentiels et problèmes aux limites elliptiques, Ann. Inst. Fourier 19 (1969), [BM71]., Boundary problems for pseudo-differential operators, Acta Math. 126 (1971), [BM76]., A course on Pseudo-differential Operators and their Applications, Duke University Mathematics Series II, [B-F-O81]. A. Bove, B. Franchi and E. Obrecht, A boundary value problem for elliptic equations with polynomial coefficients in a half space; I. Pseudodifferential operators and function spaces, Boll. Un. Mat. Ital. B 18 (1981), 25 45; II. The boundary value problem, Boll. Un. Mat. B 18 (1981), [C63]. A. P. Calderón, Boundary value problems for elliptic equations, Outlines Joint Symposium PDE Novosibirsk, Acad. Sci. USSR Siberian Branch, Moscow, 1963, pp [C-E71]. Čan Zui Ho and G. Eskin, Boundary value problems for parabolic systems of pseudo-differential equations, Dokl. Akad. Nauk SSSR 198 (1971), 50 53; Soviet Math. Dokl 12 (1971), [Ca85]. C. Cancelier, Problèmes aux limites pseudodifférentiels donnant lieu au principe de maximum, Comm. Part. Diff. Equ. 11 (1985), [Co79]. H. O. Cordes, Elliptic Pseudo-differential Operators An Abstract Theory, Lecture Note 756, Springer Verlag, Berlin, [D77]. Y. Demay, Paramétrix pour des systèmes hyperboliques du premiér ordre à multiplicité constante, J. Math. pures et appl. 56 (1977), [De75]. A. Demidov, Asymptotic behavior of the solution of a boundary value problem for elliptic pseudodifferential equations with a small parameter multiplying the leading operator, Trudy Moskov. Mat. Obsv. 32 (1975); Trans. Moscow Mat. Soc 32 (1975), [Dr74]. Ja. M. Drin, Study of one class of parabolic pseudodifferential operators in the spaces of Hölder s functions, Notes of the Ukrainian Academy of Sciences, Series A no. 1 (1974), 19 22, (Russian, English summary). [Dr74 ]., On the structure of pseudodifferential operators with generalizedhomogeneous characters. Notes of the Ukrainian Academy of Sciences, Series A, (Physical-technical and mathematical sciences) 7 (1974), , (Russian, English summary). [Dr77]., Fundamental solution of the Cauchy problem for one class of parabolic pseudodifferential equations, Notes of the Ukraninian Academy of Sciences, Series A (physical-mathematical and technical sciences) 3 (1977), , (Russian). [D-G75]. J. J. Duistermaat and V. Guillemin, The spectrum of positive elliptic operators and elliptic bicharacteristics, Inventiones Math 29 (1975),

3 508 BIBLIOGRAPHY [Du77]. J. Dunau, Fonctions d un opérateur elliptique sur une variété compacte, J. Math. pures et appl. 56 (1977), [D-S57]. N. Dunford and J. Schwartz, Linear Operators, Part I: General Theory, Interscience Publishers, New York, [Ei69]. S. D. Eidelman, Parabolic Systems, North-Holland Publ. Co., Amsterdam, [E-D74]. S. D. Eidelman and Ja. M. Drin, Necessary and sufficient conditions for the stability of solutions of the Cauchy problem for parabolic pseudodifferential equations. Approximation Methods in Mathematical Analysis, Kiev State Pedagogical Institute, Kiev (1974), 60 71, (Russian). [E-D81]., Construction and investigation of classical fundamental solutions for one-dimensional Cauchy problems for parabolic pseudodifferential equations, Mathematical Investigations, Academy of Science of the Moldavian Republic (1981), 18 33, (Russian). [E75]. G. I. Eskin, Asymptotics near the boundary of spectral functions of elliptic self-adjoint boundary problems, Israel J. Math. 22 (1975), [E81]., Boundary Value Problems for Elliptic Pseudodifferential Equations, Transl. Math. Monogr. 52, Amer. Math. Soc., Providence, [F-J67]. E. B. Fabes and M. Jodeit, Boundary value problems for second order parabolic equations, Amer. Math. Soc. Proc. Symp. Pure Math. 10 (1967), [F-R67]. E. B. Fabes and N. M. Riviére, Symbolic calculus of kernels with mixed homogeneity, Amer. Math. Soc. Proc. Symp. Pure Math. 10 (1967), [Fe74]. B. V. Fedosov, Analytical formulas for the index of elliptic operators, Trudy Mosk. Mat. Obsv. 30 (1974), ; Trans. Moscow Math. Sov 30 (1974), [Fr79]. L. S. Frank, Coercive singular perturbations; I: A priori estimes, Ann. Mat. pura appl. 119 (1979), [Fr90]., Singular Perturbations I, Spaces and Singular Perturbations on Manifolds Without Boundary, North-Holland, Amsterdam, [Fr95]., Singular Perturbations II, in preparation. [F-W82]. L. S. Frank and W. D. Wendt, Coercive singular perturbations; II: Reduction to regular perturbations and applications, Comm. Part. Diff. Equ. 7 (1982), [F-W82 ]., Coercive singular perturbations; II: Reduction and convergence, J. Math. Anal. Appl. 88 (1982), , [Much of the material here is repeated verbatim in [Fr-W82].]. [F-W84]., Coercive singular perturbation; III: Wiener-Hopf operators, J. d Analyse Math 43 (1984), [F-W85]., Erratum, Comm. Part. Diff. Equ. 10 (1985), [Fra85]. J. Franke, Besov-Triebel-Lizorkin spaces and boundary value problems, Seminar Analysis 1984/85, Karl Weierstrass Institut für Math., Berlin DDR, 1985, pp [Fra86]. J. Franke, Elliptische Randwertprobleme in Besov-Triebel-Lizorkin-Raümen, Dissertation, Friedrich Schiller Universität Jena [Fri69]. A. Friedmann, Partial Differential Equations, Holt, Rinehart and Winston, New York, [F-S70]. D. Fujiwara and N. Shimakura, Sur les problèmes aux limites stablement variationnels, J. Math. Pures et appl. 49 (1970), 1 28.

4 BIBLIOGRAPHY 509 [Gå53]. L. Gårding, Dirichlet s problem for linear elliptic partial differential equations, Math. Scand. 1 (1953), [Gå53 ]., On the asymptotic distribution of the eigenvalues and eigenfunctions of elliptic differential operators, Math. Scand. 1 (1953), [Gi81]. Y. Giga, The Stokes operator in L r spaces, Proc. Japan Acad. 57, Ser. A (1981), [Go60]. I. C. Gohberg, On the theory of multidimensional singular integral equations, Dokl. Akad. Nauk SSSR 133 (1960), [Go-K69]. I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators, Amer. Math. Soc. Transl. Math. Monogr. 18, Rhode Island, [Gos81]. M. de Gosson, Paramétrix de transmission pour des opérateurs de type parabolique et applications au problème de Cauchy microlocal, C. R. Acad. Sci. Paris (Sér.A) 292 (1981), [Grl69]. W. M. Greenlee, Rate of convergence in singular perturbations, Ann. Inst. Fourier 18 (1969), [Grei67]. P. Greiner, An asymptotic extension for the heat equation, Arch. Rat. Mech. Anal 25 (1967), [Gri67]. P. Grisvard, Caractérisation de quelques espaces d interpolation, Arch. Rat. Mech. Anal. 25 (1967), [G-G77]. G. Grubb and G. Geymonat, The essential spectrum of elliptic systems of mixed order, Math. Ann. 227 (1977), [G-G79]., Eigenvalue asymptotics for selfadjoint elliptic mixed order systems with non-empty essential spectrum, Boll. U. M. I. 16-B (1979), [G68]. G. Grubb, A characterization of the non-local boundary value problems associated with an elliptic operator, Ann. Scuola Norm. Sup. Pisa 22 (1968), , Stanford University dissertation [G70]., Les problèmes aux limites généraux d un opérateur elliptique, provenant de la théorie variationnelle, Bull. Sc. Math 94 (1970), [G71]., On coerciveness and semiboundedness of general boundary problems, Isr. J. Math. 10 (1971), [G73]., Weakly semibounded boundary problems and sesquilinear forms, Ann. Inst. Fourier Grenoble 23 (1973), [G73 ]., Inequalities for boundary value problems for systems of partial differential operators, Astérisque 2-3 (1973), [G74]., Properties of normal boundary problems for elliptic even-order systems, Ann. Scuola Norm. Sup. Pisa 1(ser.IV) (1974), [G77]., Spectral asymptotics for Douglis-Nirenberg elliptic and pseudo-differential boundary problems, Comm. Part. Diff. Equ. 2 (1977), [G77 ]., Boundary problems for systems of partial differential operators of mixed order, J. Functional Analysis 26 (1977), [G78]., Remainder estimates for eigenvalues and kernels of pseudo-differential elliptic systems, Math. Scand. 43 (1978), [G78 ]., Estimation du reste dans l étude des valeurs propres des problèmes aux limites pseudo-différentiels auto-adjoints, C. R. Acad. Sci. Sér. A 287 (1978), [G79]., On Pseudo-Differential Boundary Problems, Reports, Copenhagen University Publication Series 2 (1979); 1, 2, 7 8 (1980). [G79 ]., Estimation du reste dans l étude des valeurs propres des problèmes aux limites pseudo-différentiels elliptiques, Sém. Goulaouic-Schwartz , Palaiseau 1979.

5 510 BIBLIOGRAPHY [G80]., A resolvent construction for pseudo-differential boundary value problems, with applications, 18th Scandinavian Congr. Math. Proceedings, Birkhäuser, Boston, 1980, pp [G81]., Problèmes aux limites dépendant d un paramètre, C. R. Acad. Sci. Paris Sér.I) 292 (1981), [G81 ]., La résolvante d un problème aux limites pseudo-differéntiel elliptique, C. R. Acad. Sci. Paris (Sér.I) 292 (1981), [G82]., The heat equation associated with a pseudo-differential boundary problem, Seminar Analysis , Akad. Eiss. Berlin, 27 41; Also available as Preprint, Copenhagen Univ. Math. Dept. 2 (1982). [G83]., On the spectral theory of pseudo-differential elliptic boundary problems, Partial Differential Equations 1978, Banach Center Publications 10,; PWN-Polish Scientific Publishers, Warsaw (1983), [G84]., Singular Green operators and their spectral asymptotics, Duke Math. J. 51 (1984), [G84 ]., Remarks on trace estimates for exterior boundary problems, Comm. Part. Diff. Equ. 9 (1984), [G85]., Une méthode pseudo-différentielle pur les perturbations singuliéres elliptiques, C. R. Acad. Sci. Paris (Sér.I) 301 (1985), [G85 ]., Trace estimates for exterior boundary problems associated with the Schrödinger operator, Schrödinger operators Aarhus 1985, Lecture Notes in Math. vol. 1218, Springer Verlag, 1986, pp [G86]., Functional Calculus of Pseudo-Differential Boundary Problems, Progress in Mathematics, vol. 65, Birkhäuser, Boston, 1986, 512 pp. [G87]., Complex powers of pseudo-differential boundary value problems with the transmission property, Pseudo-Differential Operators Oberwolfach 1986, Lecture Notes in Math. vol. 1256, Springer Verlag, 1987, pp [G90]., Pseudo-differential boundary problems in L p spaces, Comm. Part. Diff. Eq. 15 (1990), [G91]., Parabolic pseudo-differential boundary problems and applications, Microlocal Analysis and Applications, Montecatini Terme, 1989, by J. M. Bony, G. Grubb, L. Hörmander, H. Komatsu, J. Sjöstrand (eds. L. Cattabriga and L. Rodino), Lecture Notes in Math. vol. 1495, Springer Verlag, Heidelberg, 1991, pp [G91 ]., Initial value problems for the Navier-Stokes equations with Neumann conditions, The Navier-Stokes equations II Theory and numerical methods, Proceedings Oberwolfach 1991, Lecture Notes in Math. vol. 1530, Springer Verlag, 1992, pp [G92]., Heat operator trace expansions and index for general Atiyah- Patodi-Singer problems, Comm. P. D. E. 17 (1992), [G94]., Nonhomogeneous Navier-Stokes problems in L p Sobolev spaces over interior and exterior domains, to appear in proceedings of Oberwolfach meeting 1994 Navier-Stokes problems III. [G95]., Parameter-elliptic and parabolic pseudodifferential boundary problems in global L p Sobolev spaces, Math. Zeitschrift 218 (1995), [G95 ]., Nonhomogeneous time-dependent Navier-Stokes problems in L p Sobolev spaces, Diff. and Int. Eq. 8 (1995), [G-H90]. G. Grubb and L. Hörmander, The transmission property, Math. Scand. 67 (1990), [G-K93]. G. Grubb and N. J. Kokholm, A global calculus of parameter-dependent

6 BIBLIOGRAPHY 511 pseudodifferential boundary problems in L p Sobolev spaces, Acta Mathematica 171 (1993). [G-Se95]. G. Grubb and R. T. Seeley, Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems, Inventiones Math. 121 (1995), [G-Se95 ]., Zeta and eta functions for Atiyah-Patodi-Singer operators, J. Geom. Analysis (to appear). [G-So87]. G. Grubb and V. A. Solonnikov, Reduction of basic initial-boundary value problems for the Stokes equation to initial-boundary value problems for systems of pseudodifferential equations, Zap. Nauchn. Sem. L.O.M.I. 163 (1987), 37 48; =J. Soviet Math. 49 (1990), [G-So89]., Reduction of basic initial-boundary value problems for the Navier- Stokes equations to nonlinear parabolic systems of pseudo-differential equations, Zap. Sem. Nauchn. L.O.M.I. 171 (1989), 36 52; =J. Soviet Math. 56 (1991), [G-So90]., Solution of parabolic pseudo-differential initial-boundary value problems, J. Diff. Equ. 87 (1990), [G-So91]., Boundary value problems for the nonstationary Navier-Stokes equations treated by pseudo-differential methods, Math. Scand. 69 (1991), [H-K71]. K. Hayakawa and H. Kumano-go, Complex powers of a system of pseudodifferential operators, Proc. Japan Acad. 47 (1971), [He84]. B. Helffer, Théorie spectrale pour des opérateurs globalement elliptiques, Asterisque 112, Société Mathématique de France, [H-P57]. E. Hille and R. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc. Colloq. Publ. 31, Providence, [Hu66]. D. Huet, Remarque sur un theorème d Agmon et applications à quelques problèmes de perturbation singulières, Boll. Un. Mat. Ital. 21 (1966), [Hu68]., Perturbations singulières et régularité, C. R. Acad. Sci. Paris (Sér.A) 266 (1968), [Hu77]., Décomposition spectrale et opérateurs, Presses universitaires de France, Paris, [Hu79]., Approximation d un espace de Banach et perturbations singulières, C. R. Acad. Sci. Paris 289 (Sér.A) (1979), [Hu81]., Proper approximation of a normed space and singular perturbations, Analytical and Numerical Approaches to Asymptotic Problems in Analysis, North Holland Publ. Co., 1981, pp [Hu85]., Convergence propre et perturbations singulières coercives, C. R. Acad. Sci. Paris 301 (Sér.I) (1985), ; Stabilité inverse d une famille d opérateurs opérant dans des espaces normés et dépendant d un paramètre, ibid., [H58]., On the regularity of solutions of boundary problems, Acta Math 99 (1958), [H63]. L. Hörmander, Linear Partial Differential operators, Springer Verlag, New York, [H65]., Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), [H66]., Pseudo-differential operators and non-elliptic boundary problems, Ann. of Math. 83 (1966),

7 512 BIBLIOGRAPHY [H66 ]., On the Riesz means of spectral functions and eigenfunction expansions for elliptic differential operators, Belfer Grad. School Sci. (Yeshiva Univ.) Conf. Proceedings 2 (1966), [H67]., Pseudo-differential operators and hypoelliptic equations, Proc. Symp. Pure Math., vol. 10, 1967, pp [H68]., The spectral function of an elliptic operator, Acta Math. 121 (1968), [H71]., Fourier integral operators I, Acta Math. 127 (1971), [H79]., The Weyl calculus of pseudo-differential operators, Comm. Pure Appl. Math 32 (1979), [H85]., The Analysis of Linear Partial Differential Operators, Springer Verlag, Berlin, , (the present work mostly uses Volume III). [Iv80]. V. Ja. Ivrii, Second term of the spectral asymptotic expansion of the Laplace- Beltrami operator on manifolds with boundary and for elliptic operators acting in fiberings, Dokl. Akad. Nauk SSSR 250 (1980); = Soviet Math. Dokl. 21 (1980), [Iv82]., Precise spectral asymptotics for elliptic operators acting in fiberings, Funkts. Anal. Prilozhen 16 No. 2 (1982); 30 38=Funct. Analysis Appl. 16 (1983), [Iv84]., Precise spectral asymptotics for elliptic operators. Lecture Notes in Math. 1100, Springer Verlag, Berlin, [I-I81]. C. Iwasaki and N. Iwasaki, Parametrix for a degenerate parabolic equation and its application to the asymptotic behavior of spectral functions for stationary problems, Publ. R.I.M.S. Kyoto 17 (1981), [Jd67]. M. Jodeit, Symbols of parabolic singular integrals, Amer. Math. Soc. Proc. Symp. Pure Math 10 (1967), [Jn95]. J. Johnsen, Elliptic boundary problems and the Boutet de Monvel calculus in Besov and Triebel-Lizorkin spaces, Math. Scand. (to appear). [Ka66]. T. Kato, Perturbation Theory for Linear Operators, Springer Verlag, Berlin, [K-N65]. J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), [Koz81]. A. Kozhevnikov, Remainder estimates for eigenvalues and complex powers of the Douglis-Nirenberg elliptic systems, Comm. Part. Diff. Equ. 6 (1981), [Koz91]., Diagonalization of systems, elliptic in the Douglis-Nirenberg sense, on manifold with boundary, Funct. Analysis Appl. 25 (1991), [Koz95]., Asymptotics of the spectrum of Douglis-Nirenberg ellitic operator on closed manifold, Math. Nachr. (to appear). [Kol79]. V. A. Kozlov, Spectral asymptotics for non-semibounded elliptic systems, Vestnik Leningrad 1 (1979), [Kol83]., Estimates of the remainder in formulas for the asymptotic behavior of the spectrum for linear operator bundles, Funkts. Anal. Prilozhen 17 No. 2 (1983), 80 81; Funct. Analysis Appl. 17 (1983), [Kr47]. M. G. Krein, Theory of self-adjoint extensions of symmetric semi-bounded operators and applications I, Mat. Sb 20: 62 (1947), , (Russian). [L-S-U67]. O. A. Ladyzenskaya, V. A. Solonnikov and N. N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow, 1967; Amer. Math. Soc. Translation, Providence, [Lp77]. A. A. Laptev, Spectral asymptotics of a composition of pseudo-differential operators and reflections from the boundary, Dokl. Akad. Nauk SSSR 236

8 BIBLIOGRAPHY 513 (1977), ; Soviet Math. Dokl 18 (1977), [Lp81]., Spectral asymptotics of a class of Fourier integral operators, Trudy Mosk. Mat. Obsv. 43 (1981), ; Trans. Moscow Math. Soc. (1983), [Ls77]. R. Lascar, Propagation des singularités des solutions des équations pseudodifférentielles quasi-homogènes, Ann. Inst. Fourier 27 (1977), [Le84]. S. Z. Levendorskii, Asymptotic behavior of the spectrum of problems of the form Au = tbu for operators that are elliptic in the Douglis-Nirenberg sense, Funkts. Anal. Prilozhen 18 (No. 3) (1984), 84 85; Funct. Analysis Appl. 18 (1984), [Le85]., Asymptotics of the spectrum of linear operator pencils, Mat. Sbornik 124 (166) (1984), ; Math. USSR Sbornik 52 (1985), [Le89]., Asymptotics of the spectrum of operators elliptic in the Douglis- Nirenberg sense, Trans. Moscow Math. Soc. 52 (1990(1989)), [Le90]., Asymptotic Distribution of Differential Operators, Kluwer, Dordrecht, [L-M68]. J. L. Lions and E. Magenes, Problèmes aux Limites non homogènes et applications, 1, Editions Dunod, Paris, [L-M68 ]., Problèmes aux limites non homogènes et applications, 2, Editions Dunod, Paris, [M-M82]. A. S. Markus and V. I. Matsaev, Comparison theorems for spectra of linear operators, and spectral asymptotics, Trudy Mosk. Mat. Obsv. 45 (1982), ; Trans. Moscow Math. Soc. (1984), [M81]. R. Melrose, Transformation of boundary problems, Acta Math. 147 (1981), [M84]., The trace of the wave group, Amer. Math. Soc. Contemporary Math. 27 Microlocal Analysis (1984), [M92]., Calculus of conormal distributions on manifolds with corners, International Math. Res. Notes 3 (1992), [M95]., Differential Analysis on Manifolds with Corners (to appear). [Me83]. G. Métivier, Estimation du reste en théorie spectrale, Rend. Sem. Mat. Univ. Politec., Torino (1983); Special Issue, [Mo82]. A. Mohamed, Etude spectrale d opérateurs hypoelliptiques à caractéristiques multiples I, Ann. Inst. Fourier (Grenoble) 32 (1982), [Mo83]., Etude spectrale d opérateurs hypoelliptiques à caractéristiques multiples II, Comm. Part. Diff.. Equ. 8 (1983), [Mo84]., Comportement asymptotique, avec estimation du reste, des valeurs propres d une classe d opérateurs pseudo-différentiels sur R n, C. R. Acad. Sci. Paris (Sér. I) 299 (1984), [Ni73]. L. Nirenberg, Lectures on Linear Partial Differential Equations, Amer. Math. Soc. Regional Conf. Series 17, Providence, [Nm79]. T. Nambu, Feedback stabilization for distributed parameter systems of parabolic type, J. Diff. Equ. 33 (1979), [Ng73]. M. Nagase, On the asymptotic behavior of resolvent kernels for elliptic operators, J. Math. Soc. Japan 25 (1973), [Ng77]., The L p boundedness of pseudo-differential operators with nonregular symbols, Comm. Part. Diff. Equ. 2 (1977), [N-S70]. M. Nagase and K. Shinkai, Complex powers of non-elliptic operators, Proc. Japan Acad. 46 (1970),

9 514 BIBLIOGRAPHY [Pa65]. V. I. Paraska, On asymptotics of eigenvalues and singular numbers of linear operators which increase smoothness, Mat. Sb. 68 (110) (1965), , (Russian). [Pe91]. M. Pedersen, Pseudodifferential perturbations and stabilization of distributed parameter systems: Dirichlet feedback control problems, SIAM J. Contr. Optim. 29 (1991), [PL81]. Pham The Lai, Meilleures estimations asymptotiques des restes de la fonction spectrale et des valeurs propres relatifs au laplacien, Math. Scand. 48 (1981), [Ph59]. R. S. Phillips, Dissipative operators and hyperbolic systems of partial differential equations, Trans. Amer. Math. Soc. 90 (1959), [Pi70]. A. Piriou, Une classe d opérateurs pseudo-différentiels du type de Volterrra, Ann. Inst. Fourier 20 (1970), [Pi71]., Problèmes aux limites généraux pour des opérateurs différentiels paraboliques dans un domaine borné, Ann. Inst. Fourier 21 (1971), [Pl61]. Å. Pleijel, Certain indefinite differential eigenvalue problems the asymptotic distribution of their eigenfunctions, Part. Diff Equ. and Continuum Mech., Wisconsin Press, Madison (1961), [Pu89]. V. T. Purmonen, Parabolic pseudo-differential initial-boundary value problems, Math. Scand. 65 (1989), [Pu90]., On a complete initial-boundary value problem for parabolic pseudodifferential, Math. Scand. 67 (1990), [Re80]. S. Rempel, An analytical index formula for elliptic pseudo-differential boundary problems I, Math. Nachr. 94 (1980), [R-S82]. S. Rempel and B.-W. Schulze, Index Theory of Elliptic Boundary Problems, Akademie-Verlag, Berlin, [R-S82 ]., Parametrices and boundary symbolic calculus for elliptic boundary problems without the transmission property, Math. Nachr. 105 (1982), [R-S83]., Complex powers for pseudo-differential boundary problems I, Math. Nachr. 111 (1983), [R-S84]., Complex powers for pseudo-differential boundary problems II, Math. Nachr. 116 (1984), [Ro78]. D. Robert, Propriétés spectrales d opérateurs pseudo-différentiels, Comm. Part. Diff. Equ. 3 (1978), [Ro78 ]., Developpement asymptotique du noyau résolvant d opérateurs elliptiques, Osaka J. Math. 15 (1978), [Sr87]. E. Schrohe, Spaces of weighted symbols and weighted Sobolev spaces on manifolds, Pseudo-differential operators, Springer Lecture Note no. 1256, Heidelberg, 1987, pp [Sr91]., A pseudodifferential calculus for weighted symbols and a Fredholm criterion for boundary value problems on noncompact manifolds, Habilitationsschrift, Univ. of Mainz [Sr92]., Functional calculus and Fredholm criteria for boundary value problems on noncompact manifolds, Operator Calculus and Spectral Theory (Lambrecht 1991), Oper. Thry. Adv. Appl. 57, Birkhäuser, Basel, pp [Sr94]., A characterization of the uniform transmission property for pseudodifferential operators, Pseudo-Differential Calculus and Mathematical Physics, Advances in P.D.E. vol. 5, Akademie Verlag, Berlin, pp

10 BIBLIOGRAPHY 515 [S-S94]. E. Schrohe and B.-W. Schulze, Boundary value problems in Boutet de Monvel s algebra for manifolds with conical singularities, Pseudo-Differential Calculus and Mathematical Physics, Advances in P.D.E. vol. 5, Akademie Verlag, Berlin, pp [Sl79]. B.-W. Schulze, Adjungierte elliptische Randwertprobleme, Math. Nachr. 89 (1979), [Sl91]., Pseudo-Differential Operators on Manifolds with Singularities, North-Holland, Amsterdam, [Sl94]., Pseudo-Differential Boundary Value Problems, Conical Singularities and Asymptotics, Akademie Verlag, Berlin, [Sw66]. L. Schwartz, Théorie des Distributions, Hermann, Paris, [Se64]. R. T. Seeley, Extension of C functions, Proc. Amer. Math. Soc. 15 (1964), [Se65]., Refinement of the functional calculus of Calderon and Zygmund, Proc. Konikl. Nederl. Akad. Wetensch. 68 (1965), [Se66]., Singular integrals and boundary value problems, Amer. J. Math. 88 (1966), [Se67]., Complex powers of an elliptic operator, Amer. Math. Soc. Proc. Symp. Pure Math. 10 (1967), [Se69]., Topics in pseudo-differential operators, C.I.M.E., Conf. on Pseudo- Differential Operators, Edizioni Cremonese, Roma, 1969, pp [Se69 ]., The resolvent of an elliptic boundary problem, Amer. J. Math. 91 (1969), [Se69 ]., Analytic extension of the trace associated with elliptic boundary problems, Amer. J. Math. 91 (1969), [Se71]., Norms and domains of the complex powers A z B, Amer. J. Math. 93 (1971), [Se72]., Interpolation in L p with boundary conditions, Studia Math. 44 (1972), [Se78]., A sharp asymptotic remainder estimate for the eigenvalues of the Laplacian in a domain of R 3, Adv. in Math. 29 (1978), [Sh78]. M. A. Shubin, Pseudodifferential Operators and Spectral Theory, Nauka, Moscow, 1978, (Russian). [So65]. V. A. Solonnikov, On the Boundary Value Problems for Linear Parabolic Systems of Differential Equations of General Form, vol. 83, Proc. Stekl. Inst. of Math., Leningrad, [St51]. N. Steenrod, The Topology of Fibre Bundles, Princeton University Press, [Str72]. R. S. Strichartz, A functional calculus for elliptic pseudo-differential operators, Amer. Math.vol94 (1972), [Tan79]. H. Tanabe, Equations of Evolution, Pitman Publishing Ltd., London, [Tay81]. M. E. Taylor, Pseudodifferential Operators, Princeton University Press, New Jersey, [Tre67]. F. Treves, Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, [Tre80]., Introduction to Pseudodifferential and Fourier Integral Operators, 1-2, Plenum Press, New York, [Tri78]. H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland Publ. Co., Amsterdam, New York, [Trg79]. R. Triggiani, On Nambu s stabilization problem for diffusion processes, J. Diff. Eq. 33 (1979),

11 516 BIBLIOGRAPHY [Va83]. D. G. Vasiliev, Binomial asymptotic of the spectrum of a boundary value problem, Funkts. Analysis Prilozhen 17 No. 4 (1983), 79 81; Funct. Anal. Appl. 17 (1983), [Va84]., Two-term asymptotics of the spectrum of a boundary-value problem under an interior reflection of a general form, Funkts. Analys. Prilozhen 18 No. 4 (1984), 1 13; Funct. Analysis Appl. 18 (1984), [Vi52]. M. I. Vishik, On general boundary value problems for elliptic differential equations, Trudy Moskov. Mat. Onsv. 1 (1952), ; Amer. Math. Soc. Trans. 24 (1963), [V-E66]. M. I. Vishik and G. I. Eskin, Parabolic convolution equations in a bounded domain, Mat. Sb. 71 (1966), ; Amer. Math. Soc. Transl. 95 (1970), [V-E67]., Elliptic equations in convolution in a bounded domain and their applications, Uspehi Mat. Nauk 22 (1967), 15 76; Russian Math. Surveys 22 (1967), [V-L57]. M. I. Vishik and L. Lyusternik, Regular degeneration and boundary layer for linear differential equations with small parameter, Uspekhi Mat. Nauk 12 (1957), 3 122; Amer. Math. Soc. Trans. (2) 20 (1962), [We83]. W. D. Wendt, Coercive Singularly Perturbed Wiener-Hopf Operators and Applications, Dissertation, Nijmegen, [Wi78]. H. Widom, A Szegö theorem and complete symbolic calculus for pseudodifferential operators, Ann. Math. Studies Princeton 91 Singularities (1978), [Wi80]., A complete symbolic calculus for pseudo-differential operators, Bull. Sc. Math. 104 (1980), [Wi85]., Asymptotic Expansions for Pseudo-differential Operators on Bounded Domains, Lecture Note 1152, Springer Verlag, Berlin, 1985.