Abstract:
The work establishes possible dimensions of Parseval's frame in the space of trigonometric polynomials of the form
$T_Q(x)=\sum\limits_{k\in Q}c_k e^{ikx}$ consisting of serial translations of a polynomial ($c_k\in\mathbb C$, where the finite set $Q\subset\mathbb Z$). Sufficient and necessary conditions for a system of serial translations to be a Parseval's frame are also established there. The result is applied to some particular cases.
Key words:the Parseval's frame, space of trigonometric polynomials, shifts of functions.
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