On MRAs and prewavelets based on elliptic splines
type: Item
instance of: scholarly article
title: On MRAs and prewavelets based on elliptic splines
zbMATH Open document ID: 1470.42061
author: Barbara Bacchelli
author: Milvia Rossini
published in: Results in Mathematics
publication date: 2021-07-06T00:00:00Z
review text: Firstly, \textit{C. Micchelli} et al. [Numer. Algorithms 1, No. 3, 331--351 (1991; Zbl 0765.65024)] have presented a multiresolution analysis (MRA) for elliptic \(d\)-variate splines and a dyadic prewavelet decomposition of \(L^2({\mathbb R}^d)\), \(d\ge 2\). In the paper under review, the authors present sampling functions with less restrictive assumptions on their Fourier transforms. Let \(q\) be a homogeneous, \(d\)-variate polynomial of degree \(m > d\) which vanishes only in the origin of \({\mathbb R}^d\). The authors use localized \(q\)-elliptic splines as scaling functions generating stationary MRAs of \(L^2({\mathbb R}^d)\). Then they construct \(r\)-regular prewavelet systems, where \(r=m - d - 1\). These prewavelets have \(m-1\) vanishing moments. For \(d=2\), some examples of scaling functions and prewavelets are presented.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 7368807
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: MRA
zbMATH Keywords: \(q\)-elliptic multivariate splines
zbMATH Keywords: scaling functions
zbMATH Keywords: regular prewavelets
MaRDI profile type: Publication
full work available at URL: s00025-021-01348-y
OpenAlex ID: W3126706261
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DOI: 10.1007/S00025-021-01348-Y
description: scientific article; zbMATH DE number 7368807