Periodic multiresolution analyses in the space of periodic complex-valued functions of an integer argument are studied. A characterization of multiresolution analyses in terms of the Fourier coefficients of functions forming a scaling sequence is obtained. An example of a multiresolution analysis with a scaling sequence that consists of trigonometric polynomials with a minimal possible spectrum is presented. A wavelet system associated with such multiresolution analysis is presented.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 499, 2021, pp. 7–21.
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Andrianov, P.A. Discrete Periodic Multiresolution Analysis. J Math Sci 273, 455–464 (2023). https://doi.org/10.1007/s10958-023-06512-z
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DOI: https://doi.org/10.1007/s10958-023-06512-z