Continuity of the fractional Hankel wavelet transform on Gelfand-Shilov spaces
type: Item
instance of: scholarly article
title: Continuity of the fractional Hankel wavelet transform on Gelfand-Shilov spaces
zbMATH Open document ID: 1480.42043
author: Kanailal Mahato
author: Prashant Singh
published in: Rocky Mountain Journal of Mathematics
publication date: 2021-09-10T00:00:00Z
review text: \textit{I. M. Gel'fand} and \textit{G. E. Shilov} [Generalized functions. Vol. I: Properties and operations. Translated by E. Saletan. New York, London: Academic Press (1964; Zbl 0115.33101)] introduced the notion of \(W\)-type spaces abreast of the properties of the Fourier transform on such spaces. As of now, the \(W\)-type spaces have found numerous applications in diverse aspects of science and engineering, particularly in the realm of partial differential operators. In this paper, the authors have examined the fractional Hankel wavelet transform on the Gelfand-Shilov spaces of type \(W\). To begin with, the authors have discussed some properties of the well-known fractional Hankel transform on certain \(W\)-type spaces. In the sequel, certain results regarding the continuity and boundedness properties of the fractional Hankel wavelet transform on a specific type of Gelfand-Shilov space are also presented.
reviewed by: Azhar Y. Tantary
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 43A32
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 46F05
zbMATH DE Number: 7393813
zbMATH Keywords: fractional Hankel transform
zbMATH Keywords: Wavelet transform
zbMATH Keywords: Gelfand-Shilov space
MaRDI profile type: Publication
full work available at URL: rmj.2021.51.963
OpenAlex ID: W3194708419
cites work: Q4003151
cites work: Characterizations of the Gelfand-Shilov spaces via Fourier transforms
cites work: Quasianalytic Gelfand-Shilov spaces with application to localization operators
cites work: Q4791729
cites work: Q5724171
cites work: Integral Equations Associated with Hankel Convolutions
cites work: Variation diminishing Hankel transforms
cites work: Q4308741
cites work: Fractional powers of Hankel transforms in the Zemanian spaces
cites work: Q4019434
cites work: On the boundedness result of wavelet transform associated with fractional Hankel transform
cites work: Continuity of the fractional Hankel wavelet transform on the spaces of type S
cites work: On Hankel Transformable Spaces and a Cauchy Problem
cites work: Continuous and discrete Bessel wavelet transforms.
cites work: Wavelet transform on spaces of type \(W\)
cites work: W p -Spaces and Fourier Transform
cites work: The wavelet transforms in Gelfand-Shilov spaces
cites work: The fractional wavelet transform on spaces of typeW
cites work: The fractional Hankel wavelet transformation
cites work: Two versions of fractional powers of Hankel-type transformations and pseudo-differential operators
cites work: Hankel-type integral transforms and their fractionalization: a note
cites work: Q3577689
cites work: Q5571178
DOI: 10.1216/RMJ.2021.51.963
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description: scientific article; zbMATH DE number 7393813