Abstract:
We present results on the expansion of elements of the spaces Lp(0,1), 0<p<1, 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.
Keywords:
functional systems of contractions and shifts of one function of the space Lp(0,1) with 0<p<1, Fourier-type series with integer coefficients, digital processing, information transmission.
Citation:
V. I. Filippov, “Integer expansion of elements from spaces of nonintegrable functions into Fourier-type series in systems of contractions and shifts of one function”, Trudy Inst. Mat. i Mekh. UrO RAN, 30, no. 4, 2024, 286–300
\Bibitem{Fil24}
\by V.~I.~Filippov
\paper Integer expansion of elements from spaces of nonintegrable functions into Fourier-type series in systems of contractions and shifts of one function
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2024
\vol 30
\issue 4
\pages 286--300
\mathnet{http://mi.mathnet.ru/timm2145}
\crossref{https://doi.org/10.21538/0134-4889-2024-30-4-286-300}
\elib{https://elibrary.ru/item.asp?id=75134224}
\edn{https://elibrary.ru/baigjt}
Citation in format AMSBIB
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