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Funktsional'nyi Analiz i ego Prilozheniya, 2020, Volume 54, Issue 4, Pages 56–63
DOI: https://doi.org/10.4213/faa3799 (Mi faa3799) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Spaces of Dyadic Distributions

M. A. Karapetyantsab, V. Yu. Protasovcde

a Moscow Institute of Physics and Technology, Moscow oblast, Dolgoprudnyi, Russia
b Regional Scientific and Educational Mathematical Center of Southern Federal University, Rostov-on-Don, Russia
c University of L'Aquila, L'Aquila, Italy
d Lomonosov Moscow State University, Moscow, Russia
e National Research University Higher School of Economics, Moscow, Russia
Full-text PDF (541 kB) Citations (5)
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DOI: https://doi.org/10.4213/faa3799
Abstract: This paper studies spaces of distributions on a dyadic half-line, which is the positive half-line equipped with bitwise binary addition and Lebesgue measure. We prove the nonexistence of a space of dyadic distributions which satisfies a number of natural requirements (for instance, the property of being invariant with respect to the Walsh–Fourier transform) and, in addition, is invariant with respect to multiplication by linear functions. This, in particular, is evidence that the space of dyadic distributions suggested by S. Volosivets in 2009 is optimal. We also show applications of dyadic distributions to the theory of refinement equations and wavelets on the dyadic half-line.
Keywords: dyadic half-line, distributions, Walsh functions, Walsh–Fourier transform, refinement equations, wavelets.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00469
19-04-01227
Ministry of Education and Science of the Russian Federation 5-100
Received: 20.05.2020
Revised: 16.07.2020
Accepted: 22.07.2020
English version:
Functional Analysis and Its Applications, 2020, Volume 54, Issue 4, Pages 272–277
DOI: https://doi.org/10.1134/S0016266320040048
Bibliographic databases:
Document Type: Article
UDC: 517.518+517.982.4+517.965
Language: Russian
Citation: M. A. Karapetyants, V. Yu. Protasov, “Spaces of Dyadic Distributions”, Funktsional. Anal. i Prilozhen., 54:4 (2020), 56–63; Funct. Anal. Appl., 54:4 (2020), 272–277
Citation in format AMSBIB
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\jour Funktsional. Anal. i Prilozhen.
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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