This article is cited in 1 paper

Series of Fourier type with integer coefficients by systems of dilates and translates of one function in $L_p$, $p\geq 1$

V. I. Filippov

Saratov Social-Economic Institute of Plekhanov Russian University of Economics, 89 Radishcheva str., Saratov, 410003 Russia

Abstract: We consider systems of functions obtained from dilates and translations of one function in the spaces $ L_p (0,1)$, $1 \leq p < \infty $. We obtain results on the representation with respect to these systems with integer coefficients of the Fourier type series. The approximation of the elements of the spaces $ L_p (0,1)$, $1 \leq p < \infty$, according to the proposed methods has the property of image compression, that is, many coefficients are zero in this case. These studies may be of interest to specialists in the transfer and processing of digital information.

Keywords: Functional systems of translates and dilates of one function, Fourier type series with integer coefficients, digital information processing, digital information transmission.

UDC: 517.518

Received: 25.04.2018
Revised: 25.04.2018
Accepted: 26.09.2018

DOI: 10.26907/0021-3446-2019-6-58-64

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:6, 51–57

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