Cite this article as:

Lukashenko T. P. Orthogonal Basis of Shifts in Space of Trigonometric Polynomials. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 4, pp. 367-373. DOI: https://doi.org/10.18500/1816-9791-2014-14-4-367-373

Language: 
Russian
Heading: 
Mathematics
UDC: 
517.98, 517.51

Orthogonal Basis of Shifts in Space of Trigonometric Polynomials

Authors: 
Lukashenko T. P., M. V. Lomonosov Moscow State University, 119991, Russia, 119991, Leninskie Gory, 1 , lukashenko@mail.ru
Abstract: 

The orthonormal basis of a system of shifts of one trigonometric polynomial exist in the space of complex trigonometric polynomials with components from m to n and in the space of real trigonometric polynomials with components from 0 to n. Under condition 0 < m < n there is no orthogonal basis of shifts of one trigonometric polynomial in this space real trigonometric polynomials with components from m to n. The system of shifts of two trigonometric polynomials are orthogonal basis in this space.

Key words: 
trigonometric polynomials, orthonormal basis of shifts, systems like orthogonal systems, frame of shifts
DOI: 
https://doi.org/10.18500/1816-9791-2014-14-4-367-373
References
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