Rate of convergence of wavelet series by cesaro means

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.