Eigenvalues of integral operators with smooth positive definite kernels
type: Item
instance of: scholarly article
title: Eigenvalues of integral operators with smooth positive definite kernels
zbMATH Open document ID: 0635.45001
DOI: 10.1007/BF01194301
author: Thomas Kühn
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: The author studies the asymptotic eigenvalue behaviour of integral operators with positive definite kernels compact d-dimensional infinite differentiable manifolds. The main result is: Let M be a compact d- dimensional \(C^{\infty}\)-manifold equipped with a finite Lebesgue-type measure \(\mu\) and let \(0<t<\infty\). Then for every positive kernel \(K\in C^{t,0}(M,M)\), \(\lambda_ n(T_{K,\mu})=0(n^{-t/d-1}).\) Here \(T_{k,\mu}\) is the integral operator with the kernel K and \(\lambda_ n(T_{K,\mu})\) is the eigenvalue of order n.
Mathematics Subject Classification ID: 45C05
Mathematics Subject Classification ID: 45M05
Mathematics Subject Classification ID: 45P05
zbMATH DE Number: 4034347
zbMATH Keywords: asymptotic eigenvalue behaviour
zbMATH Keywords: positive definite kernels
MaRDI profile type: Publication
cites work: Q3721171
cites work: Q3759415
cites work: Eigenvalues of Positive Definite Kernels
cites work: Eigenvalues of Positive Definite Kernels II
cites work: On the Sharpness of Weyl’s Estimate for Eigenvalues of Smooth Kernels
cites work: Q5811493
cites work: Q4169288
description: scientific article; zbMATH DE number 4034347