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Fourier-Laplace transforms and the Bergman spaces


Author: Saburou Saitoh
Journal: Proc. Amer. Math. Soc. 102 (1988), 985-992
MSC: Primary 32A35; Secondary 42A38, 42B05, 44A10
DOI: https://doi.org/10.1090/S0002-9939-1988-0934879-6
MathSciNet review: 934879
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Abstract: The Fourier-Laplace transforms on $ {R^n}(n \geq 2)$ whose images belong to the Bergman spaces are investigated from the point of view of a general theory of integral transforms. The central problems are to give the expressions of the Bergman kernels in terms of the Fourier-Laplace transforms, and to investigate the relationship between the domains and the ranges in the expressions.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0934879-6
Keywords: Fourier-Laplace transform, Bergman kernel, tube domain, convex domain, general theory of integral transforms
Article copyright: © Copyright 1988 American Mathematical Society

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