We study multidimensional periodic wavelet systems with matrix dilations. We obtain conditions sufficient for such a system to be Bessel. The conditions are given in terms of Fourier coefficients. We propose a method for constructing a wavelet Riesz basis that starts with a suitable sequence of trigonometric polynomials.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 480, 2019, pp. 48–61.
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Andrianov, P.A. Sufficient Conditions for a Multidimensional System of Periodic Wavelets to be a Frame. J Math Sci 251, 190–199 (2020). https://doi.org/10.1007/s10958-020-05080-w
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DOI: https://doi.org/10.1007/s10958-020-05080-w