Paley-Wiener theorems for the Hankel transformation
type: Item
instance of: scholarly article
title: Paley-Wiener theorems for the Hankel transformation
zbMATH Open document ID: 0828.44001
DOI: 10.1007/BF02850837
author: M. Linares
author: J. M. R. Méndez
author: Jorge J. Betancor
publication date: 1995-09-04T00:00:00Z
review text: Two theorems of the Paley-Wiener type for the Hankel transform are established. Such theorems are known for the Fourier transform. Here the authors obtain the related results for the Hankel transform recalling a suitable space of the Frechet type introduced by Zemanian. The fact of application of this space by means of the Hankel transform onto the space of entire functions being equipped with the topology induced by a special system of norms is used. The authors introduce a new two-parameter family of spaces of entire functions bounded by a power-exponential weight. Assuming that the images of the Hankel transform belong to this space or to the weighted Lebesgue space on the positive half axis the Paley-Wiener theorems give a correspondence of them to continuous or integrable functions which vanish in some infinite interval.
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 46A04
zbMATH DE Number: 792944
zbMATH Keywords: Frechet space
zbMATH Keywords: Hankel transform
zbMATH Keywords: entire functions
zbMATH Keywords: Paley-Wiener theorems
reviewed by: S. Yakubovich
MaRDI profile type: Publication
cites work: Q3819501
cites work: The Hankel Convolution and the Zemanian Spaces βμ and β'μ
cites work: Q5833361
cites work: Q3692284
cites work: Entire functions of exponential type with polynomial growth on \(\mathbb R^n_x\)
cites work: A weighted version of the Paley–Wiener theorem
cites work: The Paley-Wiener theorem with general weights
cites work: Q3471027
cites work: Q4710855
cites work: The Hankel Transformation of Certain Distributions of Rapid Growth
published in: Rendiconti del Circolo Matematico di Palermo
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description: scientific article; zbMATH DE number 792944