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Periodic Schrödinger operators on a manifold. (English) Zbl 0655.58033
The present paper treats some spectral properties of the Schrödinger operator \(-\Delta +q\) defined on an open Riemannian manifold with an isometry group \(\Gamma\) whose orbit space is compact, where the function q is supposed to be periodic under the \(\Gamma\)-action. A generalization of the Bloch’s theorem is discussed. Examples of manifolds on which the Schrödinger operators have eigenvalues are exhibited.
Reviewer: T.Kobayashi

MSC:
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
35J10 Schrödinger operator, Schrödinger equation
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