Integral Equations and Operator Theory

, Volume 69, Issue 3, pp 317-346

First online:

Toeplitz Operators with Special Symbols on Segal–Bargmann Spaces

  • K. JotsaroopAffiliated withDepartment of Mathematics, Indian Institute of Science
  • , S. ThangaveluAffiliated withDepartment of Mathematics, Indian Institute of Science Email author 

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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


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