Compactly supported multi-wavelets
type: Item
instance of: scholarly article
title: Compactly supported multi-wavelets
zbMATH Open document ID: 1247.42033
author: Wojciech Banaś
published in: Opuscula Mathematica
publication date: 2012-07-31T00:00:00Z
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 6062427
zbMATH Keywords: compactly supported multi-wavelets
zbMATH Keywords: generalization of Daubechies wavelets
zbMATH Keywords: compactly supported scaling function
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: Schmidt orthogonalization
MaRDI profile type: Publication
full work available at URL: opmath.2012.32.1.21
OpenAlex ID: W2115767511
DOI: 10.7494/OPMATH.2012.32.1.21
review text: The purpose of this paper is to give a generalization of the orthogonal compactly supported wavelets which have been constructed by Daubechies in the one-dimensional case. New compactly supported multi-wavelets in \(L^2(\mathbb R^d), d \geq 2\), are based on the one-dimensional functions, when \(d = 1\). It is demonstrated that some methods, which are useful in the construction of wavelets with compact supports at \(d = 1\), can be adapted to higher-dimensional cases. The Schmidt orthogonalization method is used, but an explanation of the reservation of the compact supports of the functions is not given. The triangular grids are not used in the construction of new functions.
reviewed by: V. L. Leontiev
description: scientific article; zbMATH DE number 6062427