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Funktsional. Anal. i Prilozhen., 2020, Volume 54, Issue 4, Pages 56–63 (Mi faa3799)  

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

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

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/faa3799

Full text: PDF file (541 kB)
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English version:
Functional Analysis and Its Applications, 2020, 54:4, 272–277

Bibliographic databases:

UDC: 517.518+517.982.4+517.965
Received: 20.05.2020
Revised: 16.07.2020
Accepted:22.07.2020

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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\paper Spaces of Dyadic Distributions
\jour Funktsional. Anal. i Prilozhen.
\yr 2020
\vol 54
\issue 4
\pages 56--63
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\crossref{https://doi.org/10.4213/faa3799}
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\jour Funct. Anal. Appl.
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\vol 54
\issue 4
\pages 272--277
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