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Chebyshevskii Sbornik, 2022, Volume 23, Issue 1, Pages 21–32
DOI: https://doi.org/10.22405/2226-8383-2022-23-1-21-32
(Mi cheb1152)
 

On construction of multidimensional periodic wavelet frames

P. A. Andrianov

Saint Petersburg State University (Saint Petersburg)
References:
Abstract: Multidimensional periodic wavelet systems with matrix dilation in the framework of periodic multiresolution analyses are studied. In this work we use notion of a periodic multiresolution analysis, the most general definition of which was given by Maksimenko and M. Skopina in [25]. An algorithmic method of constructing multidimensional periodic dual wavelet frames from a suitable set of Fourier coefficients of one function is provided. This function is used as the first function in a scaling sequence that forms two periodic multiresolution analyses, which are used to construct wavelet systems. Conditions that the initial function has to satisfy are presented in terms of a certain rate of decay of its Fourier coefficients, and also mutual arrangement of zero and non-zero coefficients.
Keywords: wavelet function, periodic multiresolution analysis, wavelet frame, Bessel system, dual frames.
Funding agency Grant number
Russian Science Foundation 18-11-00055
Received: 22.10.2021
Accepted: 27.02.2022
Document Type: Article
UDC: 517.5
Language: English
Citation: P. A. Andrianov, “On construction of multidimensional periodic wavelet frames”, Chebyshevskii Sb., 23:1 (2022), 21–32
Citation in format AMSBIB
\Bibitem{And22}
\by P.~A.~Andrianov
\paper On construction of multidimensional periodic wavelet frames
\jour Chebyshevskii Sb.
\yr 2022
\vol 23
\issue 1
\pages 21--32
\mathnet{http://mi.mathnet.ru/cheb1152}
\crossref{https://doi.org/10.22405/2226-8383-2022-23-1-21-32}
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