Essential self-adjointness of Schrödinger type operators on manifolds

Essential self-adjointness of Schrödinger type operators on manifolds (2002)

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by Maxim Braverman , Ognjen Milatovic , Mikhail Shubin

Venue:	RUSS. MATH. SURVEYS
Citations:	2 - 0 self

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@ARTICLE{Braverman02essentialself-adjointness,
    author = {Maxim Braverman and Ognjen Milatovic and Mikhail Shubin},
    title = {Essential self-adjointness of Schrödinger type operators on manifolds},
    journal = {RUSS. MATH. SURVEYS},
    year = {2002},
    volume = {57},
    pages = {641--692}
}

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Abstract

We obtain several essential self-adjointness conditions for the Schrödinger-type operator HV = D ∗ D + V, where D is a first order elliptic differential operator acting on the space of sections of a hermitian vector bundle E over a manifold M with positive smooth measure dµ, and V is a Hermitian bundle endomorphism. These conditions are expressed in terms of completeness of certain metrics on M naturally associated with HV. These results generalize the

Citations

1140	The Analysis of Linear Partial Differential Operators II (Grundlehren v. 257 - Hörmander - 1983
1058	Sobolev spaces - Adams - 1975
491	Theory of Ordinary Differential Equations - Coddington, Levinson - 1955
257	Interpolation theory, function spaces, differential operators. Second edition. Johann Ambrosius - Triebel - 1995
242	Heat kernels and Dirac operators - Berline, Getzler, et al. - 1991
227	Schrödinger operators with applications to quantum mechanics and global geometry - Cycon, Froese, et al.
211	Pseudodifferential Operators and Spectral Theory - Shubin - 2001
206	Foundations of differentiable manifolds and Lie groups - Warner - 1983
118	Eigenfunction Expansions associated with Second-order Differential Equations (Clarendon press - Titchmarsh - 1946
116	M.: The Schrödinger Equation - Berezin, Shubin - 1991
110	Sobolev spaces - Maz’ya - 1985
80	Riemannian center of mass and mollifier smoothing - Karcher - 1977
63	B.: Brownian motion and Harnack inequality for Schrödinger operators - AIZENMAN, SIMON - 1982
58	Direct methods of qualitative spectral analysis of singular differential operators - Glazman - 1963
56	Schrödinger operators with singular potentials - KATO - 1972
47	Operators Part II: Spectral Theory, Self Adjoint Operators in Hilbert Space - Dunford, Schwartz, et al. - 1963
46	Essential self-adjointness of powers of generators of hyperbolic equations - Chernoff - 1973
43	theory of elliptic operators on non-compact manifolds, Astérisque 207 - Shubin
38	Nonlinear analysis on manifolds: Sobolev spaces and inequalities - Hebey - 1999
36	Schrödinger operators with singular magnetic potentials - Leinfelder, Simader - 1981
28	An index theorem on open manifolds - Roe - 1988
26	Semiclassical asymptotics on covering manifolds and Morse inequalities - Shubin - 1996
24	Introduction to spectral theory: Selfadjoint ordinary differential operators - Levitan, Sargsjan - 1975
23	A special Stokes’s theorem for complete Riemannian manifolds - Gaffney - 1954
22	Schrödinger operators in the twentieth century - Simon - 2000
18	Spectral theory of linear differential operators and comparison algebras, London Math - Cordes - 1987
18	N.Ya.Vilenkin: “Generalized Functions, Vol.4 - Applications of Harmonic Analysis - Gel’fand - 1964
16	Fundamental properties of Hamiltonian operators of Schrödinger type - Kato - 1951
15	Uniqueness of the self-adjoint extension of singular elliptic differential operators, Arch. for Rat - Ikebe, Kato - 1962
14	A property of Sobolev spaces - Brezis, Browder - 1979
14	Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren - Friedrichs - 1934
14	The identity of weak and strong extensions of differential operators - Friedrichs - 1944
14	On the essential self-adjointness of the Schrödinger operator on a complete Riemannian manifold - Oleinik - 1993
12	Essential self-adjointness of semi-bounded magnetic Schrödinger operators on non-compact manifolds, Preprint math.SP/0007019 - Shubin - 2000
11	On the spectral theory of Schrödinger and Dirac operators with strongly singular potentials - Kalf, Schmincke, et al. - 1975
11	Remarks on essential selfadjointness of Schrödinger operators with singular electrostatic potentials - Simader - 1992
9	Self-adjointness of the Beltrami-Laplace operator on a complete paracompact manifold without boundary - Chumak - 1973
9	Note on the uniqueness of Green’s functions associated with certain differential equations - Sears - 1950
9	Classical and quantum completeness for the Schrödinger operators on noncompact manifolds. Geometric aspects of partial differential equations - Shubin - 1998
9	Essential self-adjointness of Schrödinger operators with positive potentials - Simon - 1973
9	Singuläre elliptische Differentialoperatoren in Hilbertschen Räumen - Stummel - 1956
8	Expansions in eigenfunctions of selfadjoint operators - Berezansky - 1968
8	On essential self-adjointness of semi-bounded second order elliptic operators without completeness of the Riemannian manifold - Brusentsev - 1995
8	Self-adjointness of powers of elliptic operators on noncompact manifolds - Cordes - 1972
8	Kato’s inequality and the spectral distribution of Laplacians on compact Riemannian manifolds - Hess, Schrader, et al. - 1980
8	On the essential self-adjointness of Schrödinger operators with locally integrable potentials - Kalf, Rofe-Beketov - 1998
8	On a theorem of Titchmarsh and - Levitan - 1961
8	Conditions for the self-adjointness of the Schrödinger operator - Rofe-Beketov - 1970
7	On self-adjointness of a Schrödinger operator on differential forms - Braverman - 1998
7	Sur la théorie mathématique de l’équation de Schrödinger - Carleman - 1934