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On approximation by tight wavelet frames on Vilenkin groups by Lukomskii, Sergey; Kruss, Iuliia; Vodolazov, Alexandr is a scholarly article available to read on EtoBox.

What is On approximation by tight wavelet frames on Vilenkin groups about?

We consider the approximate properties of tight wavelet frames on Vilenkin group $G$. Let $\{G_n\}_{n\in \mathbb{Z} }$ be a main chain of subgroups, $X$ be a set of characters. We define a step function $\lambda({\chi})$ that is constant on cosets ${G}_n^\bot\setminus{G}_{n-1}^\bot$ by equalities $\lambda ({G}_n^\bot\setminus{G}_{n-1}^\bot)=\lambda_n>0$ for which $\sum\frac{1}{\lambda_n}<\infty$. We find the order of approximation of functions $f$ for which $\int_X|\lambda( {\chi})\hat{f}(\chi)|^2d\nu(\chi)<\infty$. As a corollary, we obtain an approximation error for functions from Sobolev spaces with logarithmic weight.

Author

Lukomskii, Sergey; Kruss, Iuliia; Vodolazov, Alexandr

Published

2023

Language

EN