On eigenvalues of differentiable positive definite kernels
type: Item
instance of: scholarly article
title: On eigenvalues of differentiable positive definite kernels
zbMATH Open document ID: 0920.45003
DOI: 10.1007/BF01203078
author: Ching-Hua Chang
author: Chung-Wei Ha
published in: Integral Equations and Operator Theory
publication date: 1999-09-08T00:00:00Z
review text: The authors consider compact integral operators in \(L^2(0,1)\) with a Hermitian kernel \(K(x,y)\), which is positive definite and has continuous partial derivatives with respect to \(y\) up to order \(p\). It is proven that the eigenvalues \(\lambda_n\), have the asymptotics, \(\lambda_n=o(n^{-p-1}), n\to \infty\). If, in addition, the \(p-\)th derivative is Lipschitz continuous in \(y\) of order \(0<\alpha\leq 1\), then \(\lambda_n =O(n^{-p-1-\alpha}), n\to \infty\).
Mathematics Subject Classification ID: 45C05
Mathematics Subject Classification ID: 45P05
zbMATH DE Number: 1262351
zbMATH Keywords: compact integral operators
zbMATH Keywords: eigenvalue asymptotics
zbMATH Keywords: Hermitian kernel
reviewed by: Georgi E. Karadzhov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01203078
OpenAlex ID: W1968143039
description: scientific article; zbMATH DE number 1262351