The Bergman Kernel and a Generalized Fourier-Borel Transform

  • Friedrich Haslinger
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 3)


In this paper we represent the dual space of a Fréchet space of entire functions again as a space of entire functions. For this purpose we use the Bergman kernel of a certain Hilbert space. In the classical setting the exponential functions provide the isomorphism via Fourier-Borel transform. In our case we use the Bergman kernel instead of the exponential functions in order to establish the isomorphism.


Hilbert Space Exponential Function Entire Function Dual Space Toeplitz Operator 
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Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Friedrich Haslinger
    • 1
  1. 1.Institut für MathematikUniversität WienAustria

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