Parseval Frames of Serial Shifts of a Function in Spaces of Trigonometric Polynomials / A. V. Fadeeva. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2018. № 6. P. 30-36 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 239-244].

We prove the criterion of existence of a Parseval frame of a priori given dimension in the space of trigonometric polynomials of the form T_Q (x) = \sum \limits_ {k \in Q} c_k e ^ {ikx} consisting of serial shifts of a polynomial ( c_k \in \mathbb 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.

Key words: the Parseval's frame, space of trigonometric polynomials, shifts of functions.