Wavelets and Frames Based on Walsh-Dirichlet Type Kernels

Authors

  • Yu. A. Farkov Russian State Geological Prospecting University, 23, Ulitsa Miklukho - Maklaya, Moscow 117997

DOI:

https://doi.org/10.26713/cma.v1i1.108

Keywords:

Dirichlet kernel, Orthogonal polynomials, Periodic wavelets, Parseval frames, Walsh functions

Abstract

Using the Walsh-Dirichlet kernel and some of its modifications, we construct several examples of frames and periodic wavelets on the positive half-line. The corresponding algorithms for decomposition and reconstruction are also discussed. It is noted that similar results can be obtained for wavelets and frames on the Cantor and Vilenkin groups.
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Issue

Vol. 1 No. 1 (2010)

Section

Research Article

License

Creative Commons Licence 4.0 by

How to Cite

Farkov, Y. A. (2010). Wavelets and Frames Based on Walsh-Dirichlet Type Kernels. Communications in Mathematics and Applications, 1(1), 27-46. https://doi.org/10.26713/cma.v1i1.108