Toeplitz operators with special symbols on Segal-Bargmann spaces
Jotsaroop K, S. Thangavelu
TL;DR
This paper investigates the boundedness of Toeplitz operators with special symbols on various Segal-Bargmann spaces, employing Gutzmer's formula to connect these operators to Fourier multipliers across different mathematical contexts.
Contribution
It introduces a unified approach using Gutzmer's formula to characterize symbols for Toeplitz operators as Fourier multipliers on multiple Segal-Bargmann related spaces.
Findings
Identification of symbols corresponding to Fourier multipliers
Application to Fock, Hermite, and Bergman spaces
Extension to symmetric space contexts
Abstract
We study the boundedness of Toeplitz operators on Segal-Bargmann spaces in various contexts. Using Gutzmer's formula as the main tool we identify symbols for which the Toeplitz operators correspond to Fourier multipliers on the underlying groups. The spaces considered include Fock spaces, Hermite and twisted Bergman spaces and Segal-Bargmann spaces associated to Riemannian symmetric spaces of compact type.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Holomorphic and Operator Theory · Geometry and complex manifolds