The Bergman Kernel and a Generalized Fourier-Borel Transform
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.
KeywordsHilbert Space Exponential Function Entire Function Dual Space Toeplitz Operator
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