Fourier-Type Series with Integer Coefficients in Systems of Contractions and Shifts of a Single Function in Spaces L p , p ≥ 1

We consider systems of functions obtained from contractions and shifts of a single function in spaces Lp(0, 1), 1 ≤ p < ∞. We obtained the results on Fourier-type series with integer coefficients with respect to the mentioned systems. The approximation of elements of spaces Lp(0, 1), 1 ≤ p < ∞...

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Bibliographic Details
Published in:Russian mathematics 2019-06, Vol.63 (6), p.51-57
Main Author: Filippov, V I
Format: Article
Language:English
Subjects:
Coefficients
Data processing
Fourier series
Image compression
Integers
Online Access:Get full text
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Summary:We consider systems of functions obtained from contractions and shifts of a single function in spaces Lp(0, 1), 1 ≤ p < ∞. We obtained the results on Fourier-type series with integer coefficients with respect to the mentioned systems. The approximation of elements of spaces Lp(0, 1), 1 ≤ p < ∞, leads to the image compression, i.e., many coefficients vanish. Results of this paper also may be of interest for experts in digital information processing and transfer.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X19060069