Fractional wavelet frames in \(L^{2}(\mathbb{R})\)
type: Item
instance of: scholarly article
title: Fractional wavelet frames in \(L^{2}(\mathbb{R})\)
zbMATH Open document ID: 1402.42047
author: Lokenath Debnath
author: Firdous Ahmad Shah
publication date: 2018-10-19T00:00:00Z
review text: The fractional Fourier transform is a generalization of the classical Fourier transform. Similar to the Fourier transform, it does not give information about the time localization of the spectral components of the analyzed signal. As a remedy for this drawback a fractional wavelet transform had been introduced. The authors of the paper study some properties of this FrWT, namely a possibility of constructing fractional wavelet frames on the real line. They establish a necessary condition and four sufficient conditions for a fractional wavelet system \(\{\psi_{j,k}^\theta: j,k\in\mathbb Z\}\) to be a frame for \(L^2(\mathbb R)\). The results are new and interesting. The proofs are technical and written in a way that makes them difficult to understand. Some preliminary material is missing, especially, a definition of the fractional Fourier transform. Language sloppiness disturbs the reading.
reviewed by: Ilona Iglewska-Nowak
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 6958683
zbMATH Keywords: fractional wavelet
zbMATH Keywords: fractional Fourier transform
zbMATH Keywords: wavelet frame
zbMATH Keywords: fractional wavelet transform
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1515/fca-2018-0023
OpenAlex ID: W2807840356
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DOI: 10.1515/FCA-2018-0023
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published in: Fractional Calculus \ Applied Analysis
description: scientific article; zbMATH DE number 6958683