Approximation by Refinement Masks

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-05 DOI:10.1134/s0001434624030076

E. A. Lebedeva

引用次数: 0

Abstract

We construct a Parseval wavelet frame with compact support for an arbitrary continuous \(2\pi\)-periodic function \(f\), \(f(0)=1\), satisfying the inequality \(|f(x)|^2+|f(x+\pi)|^2\le 1\). The frame refinement mask uniformly approximates \(f\). The refining function has stable integer shifts.

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用细化掩模进行逼近

Abstract 我们为满足不等式 \(|f(x)|^2+|f(x+\pi)|^2\le 1\) 的任意连续 \(2\pi\)-periodic 函数 \(f\), \(f(0)=1\) 构造了一个具有紧凑支持的 Parseval 小波框架。框架细化掩码均匀地近似于 \(f\)。细化函数具有稳定的整数偏移。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.