Low-energy spectrum of Toeplitz operators: the case of wells

  • Alix Deleporte

    Université de Strasbourg, France
Low-energy spectrum of Toeplitz operators: the case of wells cover

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Abstract

In the 1980s, Helffer and Sjöstrand examined in a series of articles the concentration of the ground state of a Schrödinger operator in the semiclassical limit. In a similar spirit, and using the asymptotics for the Szegő kernel, we show a theorem about the localization properties of the ground state of a Toeplitz operator, when the minimal set of the symbol is a finite set of non-degenerate critical points. Under the same condition on the symbol, for any integer we describe the first eigenvalues of the operator.

Cite this article

Alix Deleporte, Low-energy spectrum of Toeplitz operators: the case of wells. J. Spectr. Theory 9 (2019), no. 1, pp. 79–125

DOI 10.4171/JST/241