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Mat. Zametki, 2018, Volume 103, Issue 1, Pages 101–110 (Mi mz11541)  

This article is cited in 2 scientific papers (total in 2 papers)

An Analog of Titchmarsh's Theorem for the Fourier–Walsh Transform

S. S. Platonov

Petrozavodsk State University

Abstract: Using the Fourier–Walsh transform on ${\mathbb R}_+=[0,+\infty)$, we prove a dyadic analog of the classical Titchmarsh theorem on the description of the image under the Fourier transformation of the set of functions satisfying the Lipschitz condition in $L^2$.

Keywords: Fourier–Walsh transform, Lipschitz conditions, dyadic harmonic analysis.

DOI: https://doi.org/10.4213/mzm11541

Full text: PDF file (470 kB)
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English version:
Mathematical Notes, 2018, 103:1, 96–103

Bibliographic databases:

UDC: 517.44
Received: 27.01.2017
Revised: 28.03.2017

Citation: S. S. Platonov, “An Analog of Titchmarsh's Theorem for the Fourier–Walsh Transform”, Mat. Zametki, 103:1 (2018), 101–110; Math. Notes, 103:1 (2018), 96–103

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Boudref Mohamed-Ahmed, “Titchmarsh's theorem of Hankel transform”, Dagestanskie elektronnye matematicheskie izvestiya, 2019, no. 11, 11–24  mathnet  crossref
    2. S. S. Platonov, “On the Fourier–Walsh Transform of Functions from Dyadic Dini–Lipschitz Classes on the Semiaxis”, Math. Notes, 108:2 (2020), 229–242  mathnet  crossref  crossref  mathscinet  isi  elib
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