Integer expansion of elements from spaces of nonintegrable functions into Fourier-type series in systems of contractions and shifts of one function

V. I. Filippov

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 4, pp. 286-300

Résumé

We present results on the expansion of elements of the spaces $L_p(0,1)$, $0 $, into systems of functions that are contractions and shifts of one function. New algorithms are designed for the expansion of functions into Fourier-type series in these systems with integer coefficients. The expansions produced by the proposed methods have the property of image compression, i.e., a large number of expansion coefficients are zeros. The results may be of interest to specialists in the transmission and processing of digital information and to other researchers who have a need to expand nonintegrable functions into series in systems of contractions and shifts of one function.

Détail

Keywords: functional systems of contractions and shifts of one function of the space $L_p (0,1)$ with $0
Mots-clés : information transmission.

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