“Localized” self-adjointness of Schrödinger type operators on Riemannian manifolds
نویسندگان
چکیده
منابع مشابه
J -self-adjointness of a Class of Dirac-type Operators
In this note we prove that the maximally defined operator associated with the Dirac-type differential expression M(Q) = i ( d dx Im −Q −Q − d dx Im ) , where Q represents a symmetric m × m matrix (i.e., Q(x) = Q(x) a.e.) with entries in L loc (R), is J -self-adjoint, where J is the antilinear conjugation defined by J = σ1C, σ1 = ( 0 Im Im 0 ) and C(a1, . . . , am, b1, . . . , bm) = (a1, . . . ,...
متن کاملUniformly Elliptic Operators on Riemannian Manifolds
Given a Riemannian manifold (M, g), we study the solutions of heat equations associated with second order differential operators in divergence form that are uniformly elliptic with respect to g . Typical examples of such operators are the Laplace operators of Riemannian structures which are quasi-isometric to g . We first prove some Poincare and Sobolev inequalities on geodesic balls. Then we u...
متن کاملEssential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifolds
We prove essential self-adjointness for semi-bounded below magnetic Schrödinger operators on complete Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This is an extension of the Povzner–Wienholtz theorem. The proof uses the scheme of Wienholtz but requires a refined invariant integration by parts technique, as well as a use of a family of cu...
متن کاملNumber Operators for Riemannian Manifolds
The Dirac operator d+ δ on the Hodge complex of a Riemannian manifold is regarded as an annihilation operator A. On a weighted space L2μΩ, [A,A ] acts as multiplication by a positive constant on excited states if and only if the logarithm of the measure density of dμ satisfies a pair of equations. The equations are equivalent to the existence of a harmonic distance function on M . Under these c...
متن کاملEssential self-adjointness for magnetic Schrödinger operators on non-compact manifolds
We give a condition of essential self-adjointness for magnetic Schrödinger operators on non-compact Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This condition is related to the classical completeness of a related classical hamiltonian without magnetic field. The main result generalizes the result by I. Oleinik [46, 47, 48], a shorter and...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2003
ISSN: 0022-247X
DOI: 10.1016/s0022-247x(03)00296-8