Integral Equations and Operator Theory

, Volume 69, Issue 3, pp 317–346 | Cite as

Toeplitz Operators with Special Symbols on Segal–Bargmann Spaces

Article

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.

Mathematics Subject Classification (2010)

47B35 43A85 22E30 

Keywords

Segal–Bargmann transform weighted Bergman spaces Toeplitz operators Fourier multipliers Gutzmer’s formula Hermite and Laguerre functions symmetric spaces 

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© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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