Generalized fourier transform and its applications |
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Authors: | S. V. Panyushkin |
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Affiliation: | (1) Orel State University, Russia |
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Abstract: | We consider the generalized Fourier transform treated as an operator on the dual of an arbitrary locally convex space. We give a definition of this operator and establish its basic properties. Special attention is paid to cases in which the range of the generalized Fourier transform coincides with a weighted space of entire functions. The results are applied to finding the orders and types of operators in various spaces. |
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Keywords: | locally convex space complex Fourier transform weighted space of entire functions entire operator function integral transform |
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