Geodesic
Discrete periodic multiresolution analysis
Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part I, Tome 499 (2021), pp. 7-21

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Discrete periodic multiresolution analysis. Multiresolution analyses in the space of discrete periodic complex-valued functions are studied. Characterization of a multiresolution analysis in terms of Fourier coefficients of functions that form a corresponding scaling sequence is obtained. An example of a multiresolution analysis with scaling sequence that consists of trigonometric polynomials with minimally supported spectrum is provided. 
@article{ZNSL_2021_499_a1,
     author = {P. A. Andrianov},
     title = {Discrete periodic multiresolution analysis},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--21},
     publisher = {mathdoc},
     volume = {499},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_499_a1/}
}
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P. A. Andrianov. Discrete periodic multiresolution analysis. Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part I, Tome 499 (2021), pp. 7-21. http://geodesic.mathdoc.fr/item/ZNSL_2021_499_a1/