Abstract
Orthonormal bases of consecutive shifts of one polynomial are constructed in some spaces of multidimensional trigonometric polynomials. The methods for constructing Parseval frames of consecutive translations of a polynomial in wider classes of multidimensional trigonometric polynomials are proposed.
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REFERENCES
T. P. Lukashenko, ‘‘Bases of trigonometric polynomials consisting of shifts of Dirichlet kernels,’’ Moscow Univ. Math. Bull. 69, 211–216 (2014). doi https://doi.org/10.3103/S0027132214050064
T. P. Lukashenko, ‘‘Orthogonal basis of shifts in space of trigonometric polynomials,’’ Izv. Sarat. Univ. New Ser. Ser.: Math., Mech., Inform. 14, 367–373 (2014). doi https://doi.org/10.18500/1816-9791-2014-14-4-367-373
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Fizmatlit, Moscow, 2004; Dover, 1999).
V. I. Bogachev and O. G. Smolyanov, Real and Functional Analysis (Springer, Cham, 2020). doi https://doi.org/10.1007/978-3-030-38219-3
I. Ya. Novikov, V. Yu. Protasov, and M. A. Skopina, Wavelet Theory (American Mathematical Society, Providence, RI, 2011; Fizmatlit, Moscow, 2005).
A. V. Fadeeva, ‘‘Parseval frames of serial shifts of a function in spaces of trigonometric polynomials,’’ Moscow Univ. Math. Bull. 73, 239–244 (2018). doi https://doi.org/10.3103/S0027132218060049
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Translated by A. Muravnik
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Lukashenko, T.P. Orthonormal Bases of Multidimensional Trigonometric Polynomials, Consisting of Translations of One of Them. Moscow Univ. Math. Bull. 75, 129–133 (2020). https://doi.org/10.3103/S0027132220030031
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DOI: https://doi.org/10.3103/S0027132220030031