On infinitely smooth compactly supported almost-wavelets
type: Item
instance of: scholarly article
title: On infinitely smooth compactly supported almost-wavelets
zbMATH Open document ID: 0843.42017
DOI: 10.1007/BF02362405
author: M. Z. Berkolajko
author: I. Ya. Novikov
published in: Mathematical Notes
publication date: 1996-08-11T00:00:00Z
review text: The authors construct the system \[ \Psi= \{\varphi_{0, k}, \psi_{j, k},\;j= 0, 1,\dots;\;k\in \mathbb{Z}\} \] of infinitely smooth functions with the properties (1) \quad \(\Psi\text{ is an orthonormal basis in } L_2(\mathbb{R}^1);\) (2) \quad \(\varphi_{0k}(t)= \varphi_{00}(t- k),\quad \psi_{j, k}(t)= \psi_{j, 0}(t- k2^{- j});\) (3) \quad \(\text{supp } \varphi_{00}= [- 3,0],\quad \text{supp } \psi_{j, 0}= [-(j+ 3) 2^{- j}, j2^{- j}].\) Unlike wavelets, the system \(\Psi\) is not generated by contractions and translations of one function. However, the length of the support of the functions \(\psi_{j, k}\) tends to 0 as \(j\to \infty\), and for each fixed \(j\) the functions \(\psi_{j, k}\), \(k\neq 0\), are obtained by translations of \(\psi_{j, 0}\).
reviewed by: Boris Rubin
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 830720
zbMATH Keywords: wavelets
MaRDI profile type: Publication
cites work: Wavelets with exponential localization
cites work: Orthonormal bases of compactly supported wavelets
cites work: Q3991872
cites work: Q3995454
cites work: Q3908526
cites work: Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 (R)
full work available at URL: https://doi.org/10.1007/bf02362405
OpenAlex ID: W2022955779
description: scientific article; zbMATH DE number 830720