Spectral and Eigenfunction Asymptotics in Toeplitz Quantization

Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 21)

Abstract

Toeplitz operators on quantized compact symplectic manifolds were introduced by Guillemin and Boutet de Monvel, who studied their spectral asymptotics in analogy with the theory developed by Duistermaat, Guillemin, and Hörmander for pseudodifferential operators. In this survey, we review some recent results concerning eigenfunction asymptotics in this context, largely based on the microlocal description of Szegö kernels by Boutet de Monvel and Sjöstrand, and its revisitation and generalization to the almost complex symplectic category by Shiffman and Zelditch. For simplicity, the exposition is restricted to the complex projective setting.

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© Springer International Publishing AG, a part of Springer Nature 2017

Authors and Affiliations

  1. 1.Dipartimento di Matematica e ApplicazioniUniversità degli Studi di Milano BicoccaMilanoItaly

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