Rate of convergence of wavelet series by cesaro means

TL;DR

This paper studies the convergence properties of wavelet series, focusing on pointwise convergence in Pringscheim's sense and Cesaro summability methods, to enhance understanding of wavelet series behavior.

Contribution

It introduces new results on Cesaro summability and strong Cesaro summability of wavelet series, extending convergence analysis in wavelet theory.

Findings

Established conditions for Cesaro |C,1,1| summability of wavelet series

Analyzed strong Cesaro |C,1,1| summability in wavelet expansions

Extended convergence results for orthogonal wavelet series

Abstract

Wavelet frames have become a useful tool in time freqency analysis and image processing. Many authors worked in the field of wavelet frames and obtained various necessary and sufficient conditions. Ron and Shen [17] gave a charactarization of wavelet frames. Benedetto and Treiber [3], Ron and Shen [17] presented different presentations to the wavelet frames. Any function $f \in L^2(R)$ can be expanded as an orthonormal wavelet series and pointwise convergence and uniform convergence of series have been discussed extensively by various authors [9, 17]. In this paper we investigate the pointwise convergence of orthogonal wavelet series in Pringscheim's sense. Furthermore, we investigate Cesaro $|C,1,1|$ summability and the strong Cesaro $|C,1,1|$ summability of wavelet series.