Progressive Gelfand-Shilov spaces and wavelet transforms
type: Item
instance of: scholarly article
title: Progressive Gelfand-Shilov spaces and wavelet transforms
zbMATH Open document ID: 1271.46033
DOI: 10.1155/2012/951819
author: Dušan Rakić
author: Nenad Teofanov
published in: Journal of Function Spaces and Applications
publication date: 2012-11-07T00:00:00Z
review text: The authors deal with the so-called progressive Gelfand-Shilov spaces \(S_\mu ^{\nu ,+}(\mathbb{R})\), constituted by all functions \(f\) in the usual Gelfand-Shilov space \(S_\mu ^\nu (\mathbb{R})\) such that the support of their Fourier transform \(\widehat{f}\) is contained in \([0,\infty )\). They deduce characterizations of the elements of \(S_\mu ^{\nu ,+}(\mathbb{R})\) in terms of the behavior of \(f\) and \(\widehat{f}\) from the corresponding ones for \(S_\mu ^\nu\) and give an additional localization property that shows that functions in \(S_\mu ^{\nu ,+}(\mathbb{R})\) are almost exponentially strip localized. Also, they establish continuity properties for the wavelet transform on \(S_\mu ^{\nu ,+}(\mathbb{R})\times S_\mu ^{\nu ,+}(\mathbb{R})\) and analyse the inverse wavelet transform. Finally, slightly faster decay on functions in progressive Gelfand-Shilov spaces is considered. That allows them to reformulate the previous results in the new context and obtain a control of the decay of the wavelet transform independently in each variable.
reviewed by: Lourdes Rodríguez-Mesa
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 46A13
Mathematics Subject Classification ID: 44A20
zbMATH DE Number: 6102746
zbMATH Keywords: Gelfand-Shilov spaces
zbMATH Keywords: wavelet transform
zbMATH Keywords: Fourier transform
Wikidata QID: Q58908794
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/951819
OpenAlex ID: W2064523687
cites work: Characterizations of the Gelfand-Shilov spaces via Fourier transforms
cites work: Spaces of test functions via the STFT
cites work: Q5474762
cites work: Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape
cites work: Wavelets. Tools for science and technology
cites work: Q3135829
cites work: Continuous and Discrete Wavelet Transforms
cites work: Q4490829
cites work: The wavelet transform of distributions
cites work: Multiresolution expansion, approximation order and quasiasymptotic behavior of tempered distributions
cites work: Q5447945
cites work: Q3807448
cites work: Banach spaces related to integrable group representations and their atomic decompositions. I
cites work: Banach spaces related to integrable group representations and their atomic decompositions. II
cites work: Super-exponential decay and holomorphic extensions for semilinear equations with polynomial coefficients
cites work: Q5425073
cites work: Star product algebras of test functions
cites work: Q3399282
cites work: Q2736011
cites work: Q3805282
cites work: Q3485452
cites work: Q5673937
cites work: Foundations of time-frequency analysis
cites work: Conditions for correctness in Gevrey classes of the Cauchy problem for weakly hyperbolic equations
cites work: Q4256625
cites work: Q3892728
description: scientific article; zbMATH DE number 6102746