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Eigenvalue estimates for the Dirac–Schrödinger operators

✍ Scribed by Bertrand Morel

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
121 KB
Volume
38
Category
Article
ISSN
0393-0440

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📜 SIMILAR VOLUMES

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We derive upper eigenvalue estimates for generalized Dirac operators on closed Riemannian manifolds. In the case of the classical Dirac operator the estimates on the first eigenvalues are sharp for spheres of constant curvature.

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In this paper, the periodic and the Dirichlet problems for the Schrödinger operator -(d 2 /dx 2 )+V are studied for singular, complex-valued potentials V in the Sobolev space H -a per [0, 1] (0 [ a < 1). The following results are shown: (1) The periodic spectrum consists of a sequence (l k ) k \ 0