Hankel matrix transforms and operators
type: Item
instance of: scholarly article
title: Hankel matrix transforms and operators
zbMATH Open document ID: 1309.47028
DOI: 10.1186/1029-242X-2012-92
author: Suliman Al-Homidan
published in: Journal of Inequalities and Applications
publication date: 2013-09-26T00:00:00Z
review text: The article under review concerns Hankel matrices and Hankel operators. Reviewer's remark: The paper contains errors. In particular, the paper contains the following result: Theorem 3.1. A Hankel matrix is regular if and only if (i) \(\lim_{n\to\infty}h_{n+k}=0\). (ii) \(\lim_{n\to\infty}\sum_{k=1}^\infty h_{n+k}=1\). (iii) \(\sup_n\sum_{k=1}^\infty|h_{n+k}|\leq M\). Condition (i) is very strange. Clearly, \( \lim_{n\to\infty}h_{n+k}=\lim_{n\to\infty}h_n. \) Condition (iii) does not make any sense. If the series converges, then \(\lim_{n\to\infty}\sum_{k=1}^\infty h_{n+k}=0\). Condition (iii) is also strange. Clearly, the supremum in question involves a non increasing sequence.
reviewed by: Vladimir V. Peller
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 41A35
zbMATH DE Number: 6211688
zbMATH Keywords: almost periodic Hankel matrix
zbMATH Keywords: Hankel operators
zbMATH Keywords: Hankel transforms
zbMATH Keywords: semi-periodic sequences
zbMATH Keywords: summability
Wikidata QID: Q59270692
MaRDI profile type: Publication
full work available at URL: 1029-242x-2012-92
OpenAlex ID: W2130326984
description: scientific article; zbMATH DE number 6211688