Examples of frames on the Cantor dyadic group
type: Item
instance of: scholarly article
title: Examples of frames on the Cantor dyadic group
zbMATH Open document ID: 1269.42021
published in: Journal of Mathematical Sciences (New York)
publication date: 2013-04-24T00:00:00Z
review text: This paper is divided into three sections. In the introductory first section, the author introduces notation and recalls some basic results and definitions,. In particular, the definitions of the dyadic field, the Cantor dyadic group \(G\), and the Walsh functions on \(G\) are found here. In Section 2 the definition of the generalized Walsh-Dirichlet kernel is recalled and a Parseval frame related to this kernel is obtained. Section 3 provides examples of wavelet frames in \(L^2(G)\). Here the definition of a multiresolution analysis in this setting is given, as well as analogs of Cohen's condition and Daubechies' admissible condition.
reviewed by: Richard A. Zalik
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 6156959
zbMATH Keywords: wavelets
zbMATH Keywords: frames
zbMATH Keywords: Walsh functions
zbMATH Keywords: Walsh-Dirichlet kernel
zbMATH Keywords: Cantor dyadic group
zbMATH Keywords: Vilenkin groups
author: Yuri A. Farkov
MaRDI profile type: Publication
full work available at URL: s10958-012-1046-2
OpenAlex ID: W2035567090
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DOI: 10.1007/S10958-012-1046-2
description: scientific article; zbMATH DE number 6156959