Wavelet frames on Vilenkin groups and their approximation properties-Reference-Cited by-同舟云学术

Wavelet frames on Vilenkin groups and their approximation properties

Published:2015-09 Issue:05 Volume:13 Page:1550036
ISSN:0219-6913
Container-title:International Journal of Wavelets, Multiresolution and Information Processing
language:en
Short-container-title:Int. J. Wavelets Multiresolut Inf. Process.

Author:

Farkov Yuri¹,Lebedeva Elena²³,Skopina Maria⁴

Affiliation:

1. Department of Applied Information Technology, Russian Presidential Academy of National Economy and Public Administration, Prospect Vernadskogo, 82, Moscow 119571, Russia

2. Mathematics and Mechanics Faculty, Saint Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg, 199034, Russia

3. Saint Petersburg State Polytechnic University, Polytechnicheskay 29, Saint Petersburg, 195251, Russia

4. Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg, 199034, Russia

Abstract

An explicit description of all Walsh polynomials generating tight wavelet frames is given. An algorithm for finding the corresponding wavelet functions is suggested, and a general form for all wavelet frames generated by an appropriate Walsh polynomial is described. Approximation properties of tight wavelet frames are also studied. In contrast to the real setting, it appeared that a wavelet tight frame decomposition has an arbitrary large approximation order whenever all wavelet functions are compactly supported.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Information Systems,Signal Processing

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219691315500368

Reference21 articles.

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