A class of weak dual wavelet frames for reducing subspaces of Sobolev spaces
type: Item
instance of: scholarly article
title: A class of weak dual wavelet frames for reducing subspaces of Sobolev spaces
zbMATH Open document ID: 1482.42085
DOI: 10.1155/2022/1372184
published in: Journal of Function Spaces
publication date: 2022-01-31T00:00:00Z
review text: Summary: In recent years, dual wavelet frames derived from a pair of refinable functions have been widely studied by many researchers. However, the requirement of the Bessel property of wavelet systems is always required, which is too technical and artificial. In present paper, we will relax this restriction and only require the integer translation of the wavelet functions (or refinable functions) to form Bessel sequences. For this purpose, we introduce the notion of weak dual wavelet frames. And for generality, we work under the setting of reducing subspaces of Sobolev spaces, we characterize a pair of weak dual wavelet frames, and by using this characterization, we obtain a mixed oblique extension principle for such weak dual wavelet frames.
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 7466768
zbMATH Keywords: Bessel sequences
zbMATH Keywords: Sobolev spaces
author: Jianping Zhang
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2022/1372184
OpenAlex ID: W4206302291
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description: scientific article; zbMATH DE number 7466768