Sharp inequalities of singular values of smooth kernels
type: Item
instance of: scholarly article
title: Sharp inequalities of singular values of smooth kernels
zbMATH Open document ID: 0932.45002
DOI: 10.1007/BF01225525
author: Ching-Hua Chang
author: Chung-Wei Ha
published in: Integral Equations and Operator Theory
publication date: 2000-03-13T00:00:00Z
review text: The authors consider the inequalities of singular values \(s_n(K)\) of the integral operators \(K\) with smooth \(L^2\) kernels. The singular values \(s_n(K)\) are the positive eigenvalues of the positive square root of \(K^*\)K. The inequalities are obtained and shown by examples to be sharp if the kernels satisfy also certain boundary conditions. The results of the paper are based on an idea of Gohberg-Krein by which the singular values of the integral operators are interrelated to the eigenvalues of some two point boundary value problems.
Mathematics Subject Classification ID: 45C05
Mathematics Subject Classification ID: 47A30
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 45P05
zbMATH DE Number: 1346929
zbMATH Keywords: inequalities of singular values
zbMATH Keywords: integral operators
zbMATH Keywords: eigenvalues
zbMATH Keywords: two point boundary value problems
reviewed by: Ulrich Kosel
MaRDI profile type: Publication
cites work: ESTIMATES OF SINGULAR NUMBERS OF INTEGRAL OPERATORS
cites work: Effective bounds for the singular values of integral operators
cites work: Q5571194
cites work: Eigenvalues of smooth kernels
full work available at URL: https://doi.org/10.1007/bf01225525
OpenAlex ID: W1965454755
description: scientific article; zbMATH DE number 1346929