Abstract
Abstract—We prove the criterion of existence of a Parseval frame of a priori given dimension in the space of trigonometric polynomials of the form TQ(x) =\({\sum\limits_{k \in Q} {cke} ^{ikx}}\) consisting of serial shifts of a polynomial (ck ∈ C, where Q is a finite set of integer numbers). The form of a frame of serial shifts of one function is also indicated. The result is applied to some particular cases.
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Original Russian Text © A.V. Fadeeva, 2018, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2018, Vol. 73, No. 6, pp. 30–36.
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Fadeeva, A.V. Parseval Frames of Serial Shifts of a Function in Spaces of Trigonometric Polynomials. Moscow Univ. Math. Bull. 73, 239–244 (2018). https://doi.org/10.3103/S0027132218060049
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DOI: https://doi.org/10.3103/S0027132218060049