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Article Dans Une Revue Journal of Spectral Theory Année : 2018

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

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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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Dates et versions

hal-01361623 , version 1 (19-09-2016)
hal-01361623 , version 2 (03-03-2017)
hal-01361623 , version 3 (21-04-2017)

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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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