Geodesic
On construction of multidimensional periodic wavelet frames
Čebyševskij sbornik, Tome 23 (2022) no. 1, pp. 21-32

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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. 
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P. A. Andrianov. On construction of multidimensional periodic wavelet frames. Čebyševskij sbornik, Tome 23 (2022) no. 1, pp. 21-32. http://geodesic.mathdoc.fr/item/CHEB_2022_23_1_a2/