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Asymptotic Analysis
Article . 2009
Data sources: mEDRA
https://dx.doi.org/10.48550/ar...
Article . 2008
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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On the Weyl law for Toeplitz operators

Authors: PAOLETTI, ROBERTO;

On the Weyl law for Toeplitz operators

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.

Country
Italy
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Keywords

Mathematics - Spectral Theory, Toeplitz operators, Weyl law, positive line bundle, Szegö kernel, Fourier integral operator, Mathematics - Complex Variables, Mathematics - Symplectic Geometry, FOS: Mathematics, Symplectic Geometry (math.SG), Complex Variables (math.CV), Spectral Theory (math.SP)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
7
Average
Average
Average
Green
bronze