On Fourier coefficients of continuous functions for Haar-type systems
type: Item
instance of: scholarly article
title: On Fourier coefficients of continuous functions for Haar-type systems
zbMATH Open document ID: 0794.42017
author: V. A. Goncharov
published in: Moscow University Mathematics Bulletin
publication date: 1994-04-06T00:00:00Z
review text: Let \(\{\chi (p_ n)\}\) be a Haar-type system built from the sequence \(\{p_ n\}\) \((n \in \mathbb{N})\). Two theorems about the Fourier coefficients \(a_ n(f)\) of a continuous functions \(f\) for the system \(\{\chi (p_ n)\}\) are proved. For example, if \(f \in \text{Lip} \alpha\) \((0<\alpha \leq 1)\) on \([0,1]\) and \(\sum^ \infty_{n=1} | a_ n(f) |^{2 \alpha/(2 \alpha+1)}<\infty\), then \(f(t) \equiv \text{const.}\) on \([0,1]\).
reviewed by: B. P. Osilenker
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 486800
zbMATH Keywords: Haar-type system
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: continuous functions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 486800