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

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 K we describe the first K eigenvalues of the operator.
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https://hal.archives-ouvertes.fr/hal-01361623
Contributor : Alix Deleporte Connect in order to contact the contributor
Submitted on : Friday, April 21, 2017 - 11:50:28 AM
Last modification on : Thursday, January 6, 2022 - 3:46:21 AM
Long-term archiving on: : Saturday, July 22, 2017 - 12:45:07 PM

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Alix Deleporte. Low-energy spectrum of Toeplitz operators: the case of wells. Journal of Spectral Theory, 2018, 9 (1), pp.79-125. ⟨10.4171/JST/241⟩. ⟨hal-01361623v3⟩

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