Nonuniform biorthogonal wavelets on positive half line via Walsh Fourier transform | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 29, Issue 1, 2021, Pages 1-17 PDF (2.95 M) | ||
| Document Type: Original Article | ||
| DOI: 10.1186/s42787-021-00128-5 | ||
| Authors | ||
| Owais Ahmad* 1; Neyaz A. Sheikh2; Mobin Ahmad3 | ||
| 1Department of Mathematics, National Institute of Technology, Srinagar, Jammu and Kashmir 190006, India | ||
| 2Department of Mathematics, National Institute of Technology, Srinagar, Jammu and Kashmir 190006, India | ||
| 3Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia. | ||
| Abstract | ||
| In this article, we introduce the notion of nonuniform biorthogonal wavelets on positive half line. We frst establish the characterizations for the translates of a single function to form the Riesz bases for their closed linear span. We provide the complete characterization for the biorthogonality of the translates of scaling functions of two nonuniform multiresolution analysis and the associated biorthogonal wavelet families in L2(R+). Furthermore, under the mild assumptions on the scaling functions and the corresponding wavelets associated with nonuniform multiresolution analysis, we show that the wavelets can generate Reisz bases. | ||
| Keywords | ||
| : Nonuniform biorthogonal wavelet; Nonuniform multiresolution analysis; Walsh-Fourier transform | ||
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