11-155 Vitali Vougalter

Sharp semiclassical bounds for the moments of eigenvalues for some Schroedinger type operators with unbounded potentials (157K, pdf) Oct 14, 11

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Abstract. We establish sharp semiclassical upper bounds for the moments of some negative powers for the eigenvalues of the Dirichlet Laplacian. When a constant magnetic field is incorporated in the problem, we obtain sharp lower bounds for the moments of positive powers not exceeding one for such eigenvalues. When considering a Schroedinger operator with the relativistic kinetic energy and a smooth, nonnegative, unbounded potential, we prove the sharp Lieb-Thirring estimate for the moments of some negative powers of its eigenvalues.

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