Generalized Fourier transform and its applications
type: Item
instance of: scholarly article
title: Generalized Fourier transform and its applications
zbMATH Open document ID: 1123.47029
author: S. V. Panyushkin
published in: Mathematical Notes
publication date: 2007-05-21T00:00:00Z
review text: The author studies the generalized Fourier transform treated as an operator on the dual of an arbitrary locally convex space; the kernel of this operator is an entire vector function. Such transforms and their kernels are studied in detail. First of all, the author gives a definition of this operator and establishes 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. Necessary and sufficient conditions for the coincidence are obtained. The results are illustrated by examples of specific function spaces. Finally, the results are used to find the orders and types of operators on locally convex spaces.
reviewed by: Kun Soo Chang
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 46E10
zbMATH DE Number: 5155481
zbMATH Keywords: locally convex space
zbMATH Keywords: complex Fourier transform
zbMATH Keywords: weighted space of entire functions
zbMATH Keywords: entire operator function
zbMATH Keywords: integral transform
MaRDI profile type: Publication
full work available at URL: s11006-006-0060-4
OpenAlex ID: W2058547200
cites work: Q5531375
cites work: On the Hilbert transform in the Bergman space.
cites work: Fourier-Laplace transformation of functionals on a weighted space of infinitely smooth functions
cites work: A Paley-Wiener type theorem for a weighted space of infinitely differentiable functions
cites work: Q5332414
cites work: Q5571188
cites work: Q4761704
cites work: Q3892487
cites work: Analytically Uniform Spaces and Some Applications
DOI: 10.1007/S11006-006-0060-4
description: scientific article; zbMATH DE number 5155481