Integer expansion in systems of translates and dilates of a single function

DOI10.1070/IM8921zbMath1448.42039OpenAlexW2995725047MaRDI QIDQ5118071

Vadim I. Filippov

Publication date: 4 September 2020

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/im8921

zbMATH Keywords

digital information processingmultidimensional spacesinteger Fourier coefficientsinteger expansions of functionsmultidimensional Fourier-type series

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (1)

Density of quantized approximations

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
• Multimodular spaces and their properties
• On generalization of Haar system and other function systems in spaces \(E_\phi\)
• Orthorecursive expansions with respect to subspaces
• 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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