Rate of convergence of wavelet series by cesaro means

zbMATH Open1449.42051arXiv1804.00980MaRDI QIDQ5237962

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Publication date: 25 October 2019

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 $fin{L}^2(R)$ 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.

Full work available at URL: https://arxiv.org/abs/1804.00980

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