@incollection{AST_1992__207__35_0, author = {Shubin, M. A.}, title = {Spectral theory of elliptic operators on non-compact manifolds}, booktitle = {M\'ethodes semi-classiques Volume 1 - \'Ecole d'\'Et\'e (Nantes, juin 1991)}, series = {Ast\'erisque}, pages = {35--108}, publisher = {Soci\'et\'e math\'ematique de France}, number = {207}, year = {1992}, language = {en}, url = {http://archive.numdam.org/item/AST_1992__207__35_0/} }
TY - CHAP AU - Shubin, M. A. TI - Spectral theory of elliptic operators on non-compact manifolds BT - Méthodes semi-classiques Volume 1 - École d'Été (Nantes, juin 1991) AU - Collectif T3 - Astérisque PY - 1992 SP - 35 EP - 108 IS - 207 PB - Société mathématique de France UR - http://archive.numdam.org/item/AST_1992__207__35_0/ LA - en ID - AST_1992__207__35_0 ER -
%0 Book Section %A Shubin, M. A. %T Spectral theory of elliptic operators on non-compact manifolds %B Méthodes semi-classiques Volume 1 - École d'Été (Nantes, juin 1991) %A Collectif %S Astérisque %D 1992 %P 35-108 %N 207 %I Société mathématique de France %U http://archive.numdam.org/item/AST_1992__207__35_0/ %G en %F AST_1992__207__35_0
Shubin, M. A. Spectral theory of elliptic operators on non-compact manifolds, in Méthodes semi-classiques Volume 1 - École d'Été (Nantes, juin 1991), Astérisque, no. 207 (1992), pp. 35-108. http://archive.numdam.org/item/AST_1992__207__35_0/
[1] On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, C.P.A.M. 15 (1) (1962), 119-147.
,[2] Elliptic problems with a parameter and parabolic problems of general type. Russian Math. Surveys 19 (1964), no. 3, 53-157.
, ,[3] A Lefschetz fixed point formula for elliptic complexes I., Ann. of Math. 86 (1967), 374-407.
, ,[4] Expansions in Eigenfunctions of Selfadjoint Operators. AMS Translation of Math. Monographs, Providence, Rhode Island, 1968.
,[5] The Schrödinger Equation. Kluwer, Dordrecht, 1991.
, ,[6] The fundamental group and the spectrum of the Laplacian. Comment. Math. Helv., 56 (1981), 581-598.
,[7] On the spectral theory of elliptic differential operators. I, Math. Ann. 142 (1) (1960-61), 22-130.
,[8] Finite propagation speed, kernel estimates for functions of the Laplace operator and the geometry of complete Riemannian manifolds. J. Diff. Geom. 17 (1982), 15-53.
, , ,[9] Essential self-adjointness of powers of generators of hyperbolic equations. J. Funct. Anal. 12 (1973), 401-414.
,[10] Self-adjointness of powers of elliptic operators on non-compact manifolds. Math. Ann., 195 (1972), 257-272.
,[11] Schrödinger operators. Springer, Berlin e.a., 1987.
, , , ,[12] -properties of second order elliptic operators, Bull. London Math. Soc. 17 (5) (1985), 417-436.
,[13] Symmetric hyperbolic linear differential equations. Comm. Pure Appl. Math. 7 (1954), 345-392.
,[14] The harmonic operator for exterior differential forms. Proc. Nat. Acad. Sci. USA, 37 (1951), 48-50.
,[15] A special Stokes's theorem for complete Riemannian manifolds. Ann. of Math. 60 (1954), 140-145.
,[16] Hilbert space methods in the theory of harmonic integrals. Transactions Amer. Math. Soc., 78 (1955), 587-665.
,[17] Expansion in eigenfunctions of differential and other operators. Dokl. Akad. Nauk SSSR, 103 (1955), 349-352.
, ,[18] Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators. Israel Program for Scientific Translation, Jerusalem 1965.
,[19] Curvature, diameter and Betti numbers. Comment Math. Helvetici 56 (1981), 179-195.
,[20] Structures métriques pour les variétés Riemanniennes, CEDIC/Fernand Nathan (1981).
,[21] Positive scalar curvature and the Dirac operator on complete Riemannian manifolds. Publications Mathématiques, 58 (1983), 83-196.
, ,[22] The analysis of linear partial differential operators. Berlin e.a., Springer-Verlag, vol. 1, 2 (1983)
.The analysis of linear partial differential operators. Berlin e.a., Springer-Verlag, vol. 3, 4 (1985).
.[23] Uniqueness of the self-adjoint extension of singular elliptic differential operators. Arch. Rath. Mech. Anal. 9 (1962), 77-92.
, ,[24] A remark to the preceding paper by Chernoff. J. Funct. Anal., 12 (1973), 415-417.
,[25] -theory of Schrödinger operators with a singular potential, In: Aspects of positivity in functional analysis-Proc. of a Conference in Tubingen, North Holland, Math. Studies 122 (1986), 63-78.
,[26] Periodic Schrödinger operators on a manifold. Forum Math. 1 (1989), 69-79.
, , .[27] -theory of elliptic differential operators with bounded coefficients. Vestnik Moskovskogo Universiteta, Ser. I Math. Mech. 1988, N° 4, 98-100 (in Russian).
.[28] Elliptic operators on manifolds of bounded geometry. Thesis, Moscow State University, 1987 (in Russian).
.[29] Properly supported uniform pseudo-differential operators on unimodular Lie groups. Trudy Sem. Petrovskogo 11 (1986), 74-97
, .Functional calculus of pseudo-differential operators on unimodular Lie groups. Trudy Sem. Petrovskogo 12 (1987), 164-200 (in Russian).
, .[30] On the essential self-adjointness of the Schrodinger operator on complete Riemannian manifolds. Preprint, 1991 (in Russian).
.[31] On the expansion of arbitrary functions in characteristic functions of the operator , Mat. Sb. 32 (74) (1953), 109-156; English transl.: AMS Transl. (2) 60 (1966), 1-49.
.[32] Methods of Modern Mathematical Physis. I: Functional Analysis. Academic Press, New York e.a., 1980.
, .Methods of Modern Mathematical Physis. II: Fourier Analysis, Self-Adjointness. Academic Press, New York e.a., 1975.
, .[33] An index theorem on open manifolds. I. II. J. Diff. Geom. 27 (1988), 87-113, 115-136.
.[34] Über den Laplace-Operator auf Riemannschen Mannigfaltigkeiten mit diskontinuerlichen Gruppen. Math. Nachr., 21 (1960), 132-149.
.[35] Deficiency indices and properties of spectum of some classes of differential operators. In: Spectral Theory and Differential Equations (Proc. Sympos., Dundee, 1974, dedicated to Konrad Jörgens). Lect. Notes Math., 448 (1975), 273-293.
.[36] Square-integrable solutions, self-adjoint extensions and spectrum of differential systems. In: Differ. Equations (Proc. Intern. Conf., Uppsala, 1977)
.Square-integrable solutions, self-adjoint extensions and spectrum of differential systems. In: Sympos. Univ. Upsaliensis Ann. Quingentesimum Celebrantis, No. 7, Almquist & Wiksell, Stockholm, 1977, 169-178.
.[37] Conditions for the self-adjointness of second order elliptic operators of general form. Teor. Funkcii i Funkcional. Anal. i Priložen. 17 (1973), 41-51.
, .[38] On the behaviour of the Schrödinger equation. Mat. Sbornik 42 (1957), 273-286 (in Russian).
.[39] Note on the uniqueness of Green's functions associated with certain differential equations. Canadian J. Math. 2 (1950), 314-325.
.[40] Complex powers of elliptic operators, Proc. Symp. Pure Math. 10 (1967), 288-307.
,[41] Pseudodifferential Operators and Spectral Theory. Springer-Verlag, Berlin e.a., 1987.
.[42] Theorems on the coincidence of the spectra of a pseudo-differential almost periodic operator in the spaces and . Sibirsk. Mat. Zh. 17 (1976), no. 1, 200-215.
.[43] Pseudodifference operators and their Green's functions. Math. USSR Izvestiya 26 (1986), no. 3, 605-622.
.[44] Weak Bloch property and weight estimates for elliptic operators. Séminaire Equations aux derivées partielles, 1989-1990, École Polytechnique, Exposé n. V.
.[45] On the equality between weak and strong extensions. Séminaire Equations aux derivées partielles, 1989-1990, École Polytechnique, Appendix a l'Exposé n. V.
, ,[46] Generation of analytic semigroups by strongly elliptic operators, Trans. A.M.S., 199 (1) (1974), 141-162.
,[47] -contractive projections and the heat semigroup for differential forms, J. Funct. Anal., 65 (3) (1986), 348-357.
,[48] Eigenfunction expansions associated with second-order differential equations. Part II. Oxford, 1958.
.[49] Halbbeschränkte partielle Differentialoperatoren zweiter Ordnung vom elliptischen Typus. Math. Ann. 135 (1958), 50-80.
.