JournalsjstVol. 3, No. 4pp. 465–484

Spectral estimates for Dirichlet Laplacians and Schrödinger operators on geometrically nontrivial cusps

  • Pavel Exner

    Doppler Institute for Mathematical Physics and Applied Mathematics, Prague, Czech Republic
  • Diana Barseghyan

    University of Ostrava, Czech Republic
Spectral estimates for Dirichlet Laplacians and Schrödinger operators on geometrically nontrivial cusps cover
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Abstract

The goal of this paper is to derive estimates of eigenvalue moments for Dirichlet Laplacians and Schrödinger operators in regions having infinite cusps which are geometrically nontrivial being either curved or twisted; we are going to show how those geometric properties enter the eigenvalue bounds. The obtained inequalities reflect the essentially one-dimensional character of the cusps and we give an example showing that in an intermediate energy region they can be much stronger than the usual semiclassical bounds.

Cite this article

Pavel Exner, Diana Barseghyan, Spectral estimates for Dirichlet Laplacians and Schrödinger operators on geometrically nontrivial cusps. J. Spectr. Theory 3 (2013), no. 4, pp. 465–484

DOI 10.4171/JST/51