This article is cited in 8 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.

UDC: 517.44

Received: 27.01.2017
Revised: 28.03.2017

DOI: 10.4213/mzm11541

 English version: Mathematical Notes, 2018, 103:1, 96–103

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