For citation:
Lukashenko T. P. Orthogonal Basis of Shifts in Space of Trigonometric Polynomials. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 4, pp. 367-373. DOI: 10.18500/1816-9791-2014-14-4-367-373, EDN: TAAMGR
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
01.12.2014
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Language:
Russian
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UDC:
517.98, 517.51
EDN:
TAAMGR
Orthogonal Basis of Shifts in Space of Trigonometric Polynomials
Autors:
Lukashenko T. P., Lomonosov Moscow State University
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.
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References:
- Новиков И. Я., Протасов В. Ю., Скопина М. А. Теория всплесков. М. : Физматлит, 2005. 616 с.
- Лукашенко Т. П. Ортогональные базисы сдвигов в пространствах тригонометрических многочленов // Современные проблемы теории функций и их приложения : материалы 17-й междунар. Сарат. зимн. шк. Саратов : ООО Изд-во «Научная книга», 2014. С. 163–169.
Received:
26.06.2014
Accepted:
20.10.2014
Published:
01.12.2014
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