On unbounded divergence sets of series in orthonormal bases
type: Item
instance of: scholarly article
title: On unbounded divergence sets of series in orthonormal bases
zbMATH Open document ID: 1267.42027
DOI: 10.3103/S1068362312050032
author: D. A. Karagulyan
published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences
publication date: 2013-01-15T00:00:00Z
review text: Let \(\{\psi_n(x)\}_{n=1}^\infty\), \(0\leq x \leq 1\), be an orthogonal system of continuous functions. Assuming that \(\{\psi_n\}_{n=1}^\infty\) has a localization property, the author proves the following theorem: For every \(G_\delta\)-set \(E\subset [0,1]\), there exists a series \[ \sum_{n=1}^\infty a_n \psi_n(x) \] that unboundedly diverges for \(x\in E\) and converges for \(x\notin E\).
reviewed by: Evgueni Doubtsov
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 42A20
zbMATH DE Number: 6125668
zbMATH Keywords: systems with localization property
zbMATH Keywords: divergence sets
zbMATH Keywords: \(G_{\delta}\)-sets
MaRDI profile type: Publication
cites work: On complete characterization of divergence sets of Fourier-Haar series
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cites work: Q4112399
cites work: Über Konvergenzmengen von Fourierreihen
description: scientific article; zbMATH DE number 6125668