Series with integer coefficients by systems of contractions and shifts of one function

DOI10.1134/S1995080220110074zbMath1458.94171OpenAlexW3116734587MaRDI QIDQ828160

Vadim I. Filippov

Publication date: 8 January 2021

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1995080220110074

zbMATH Keywords

\(L_p\)-spacesfunctional systemscontractions and shifts of functiondigital information processingdigital information transmissionFourier type series with integer coefficients

Mathematics Subject Classification ID

Information theory (general) (94A15) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Cites Work

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• Convergence to zero of exponential sums with positive integer coefficients and approximation by sums of shifts of a single function on the line
• On generalization of Haar system and other function systems in spaces \(E_\phi\)
• Representation in \(L_ p\) by series of translates and dilates of one function
• On the convergence of orthorecursive expansions in nonorthogonal wavelets
• Function systems obtained using translates and dilates of a single function in the paces $ E_\varphi$ with $ \lim_{t\to\infty}\frac{\varphi(t)}t=0$
• Representation systems obtained using translates and dilates of a single function in multidimensional spaces $ E_{\varphi}$

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