On a family of integral operators of Hankel type
type: Item
instance of: scholarly article
title: On a family of integral operators of Hankel type
zbMATH Open document ID: 1288.47029
author: Christoph Uebersohn
published in: Integral Equations and Operator Theory
publication date: 2013-08-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1211.5277
review text: In the paper under review, the author considers a family of integral Hankel operators \(K^{(j)}\), \(j\geq0\), on \(L^2(0,\infty)\). The operator \(K_j\) is unitarily equivalent to the Hankel operator on the Hardy class \(H^2\) on the unit circle \({\mathbb T}\) with symbol \(2z^{j+1}\chi\), where \(\chi\) is the characteristic function of the right half-circle \(\{\zeta\in{\mathbb T}:\text{Re}\zeta\geq0\}\). The author performs explicit diagonalizations of the operators \(K^{(j)}\) and proves that each \(K^{(j)}\) has simple absolutely continuous spectrum filling \([-1,1]\).
reviewed by: Vladimir V. Peller
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 6199460
zbMATH Keywords: Hankel operators
zbMATH Keywords: integral operator
zbMATH Keywords: spectrum
zbMATH Keywords: diagonalization
MaRDI profile type: Publication
OpenAlex ID: W2027888109
arXiv ID: 1211.5277
cites work: Q5827353
cites work: On Krein’s example
cites work: Q5823806
cites work: Q3241497
cites work: Q3951096
cites work: On the Hilbert Matrix, II
cites work: A commutator method for the diagonalization of Hankel operators
DOI: 10.1007/S00020-013-2069-X
description: scientific article; zbMATH DE number 6199460