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Toeplitz Operators with Special Symbols on Segal–Bargmann Spaces

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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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  1. Department of Mathematics, Indian Institute of Science, Bangalore, 560 012, India

    K. Jotsaroop & S. Thangavelu

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  1. K. Jotsaroop
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  2. S. Thangavelu
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Correspondence to S. Thangavelu.

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Jotsaroop, K., Thangavelu, S. Toeplitz Operators with Special Symbols on Segal–Bargmann Spaces. Integr. Equ. Oper. Theory 69, 317–346 (2011). https://doi.org/10.1007/s00020-010-1846-z

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  • DOI: https://doi.org/10.1007/s00020-010-1846-z

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