A Weyl law for Toeplitz operators was proved by Boutet de Monvel and Guillemin for general Toeplitz structures. In the setting of positive line bundles, we revisit this theme in light of local asymptotic techniques based on the microlocal theory of the Szego kernel. By pairing this approach with classical arguments used to estimate the spectral function of a pseudodifferential operator, we first establish a local Weyl law (that is, a pointwise estimate on the spectral function of the Toeplitz operator). The global Weyl law follows by integration.

Paoletti, R. (2009). On the Weyl law for Toeplitz operators. ASYMPTOTIC ANALYSIS, 63(1-2), 85-99 [10.3233/ASY-2008-0929].

On the weyl law for toeplitz operators

PAOLETTI, ROBERTO
2009

Abstract

A Weyl law for Toeplitz operators was proved by Boutet de Monvel and Guillemin for general Toeplitz structures. In the setting of positive line bundles, we revisit this theme in light of local asymptotic techniques based on the microlocal theory of the Szego kernel. By pairing this approach with classical arguments used to estimate the spectral function of a pseudodifferential operator, we first establish a local Weyl law (that is, a pointwise estimate on the spectral function of the Toeplitz operator). The global Weyl law follows by integration.
Articolo in rivista - Articolo scientifico
Scientifica
Toeplitz operators, Weyl law, positive line bundle, Szegö kernel, Fourier integral operator
English
85
99
Paoletti, R. (2009). On the Weyl law for Toeplitz operators. ASYMPTOTIC ANALYSIS, 63(1-2), 85-99 [10.3233/ASY-2008-0929].
Paoletti, R
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/5350
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