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

Alix Deleporte

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arXiv · 1609.05680

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

Alix Deleporte

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Abstract

In the 1980s, Helffer and Sj\"ostrand examined in a series of articles the concentration of the ground state of a Schr\"odinger operator in the semiclassical limit. In a similar spirit, and using the asymptotics for the Szeg\"o 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 K we describe the first K eigenvalues of the operator.

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BibTeX RIS

Alix Deleporte. 2016-09-19. Low-energy spectrum of Toeplitz operators: the case of wells. https://arxiv.org/abs/1609.05680

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