Integral Equations and Operator Theory

, Volume 69, Issue 3, pp 317–346

Toeplitz Operators with Special Symbols on Segal–Bargmann Spaces

Authors

  • K. Jotsaroop
    • Department of MathematicsIndian Institute of Science
    • Department of MathematicsIndian Institute of Science
Article

DOI: 10.1007/s00020-010-1846-z

Cite this article as:
Jotsaroop, K. & Thangavelu, S. Integr. Equ. Oper. Theory (2011) 69: 317. doi:10.1007/s00020-010-1846-z

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)

47B3543A8522E30

Keywords

Segal–Bargmann transformweighted Bergman spacesToeplitz operatorsFourier multipliersGutzmer’s formulaHermite and Laguerre functionssymmetric spaces

Copyright information

© Springer Basel AG 2010