Some asymptotic properties of the polylaplacian operator
type: Item
instance of: scholarly article
title: Some asymptotic properties of the polylaplacian operator
zbMATH Open document ID: 1239.34020
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-10-24T00:00:00Z
review text: The paper deals with the eigenvalue problem \[ (-1)^m\psi^{(2m)} =\lambda \psi \] on the interval \([-1, 1]\) with the boundary conditions \(\psi^{(j)}(\pm 1)=0\) \((0\leq j\leq m -1)\). The author considers the asymptotic behaviour of the eigenvalues as \(m\to \infty\). He derives strikingly simple asymptotically correct formulae for the Green's function, for the minimal eigenvalue, and for the associated eigenvector. The principal feature observed is that, for large \(m\), the solution operators can be well approximated in all Schatten norms by operators of rank 1. He also shows that a fixed lower-order perturbation term has no effect on the asymptotic behaviour of the solution operator.
Mathematics Subject Classification ID: 34B09
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 34B27
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 5962657
zbMATH Keywords: polylaplacian
zbMATH Keywords: Green's functions
zbMATH Keywords: integral operators
author: Simon P. Eveson
reviewed by: Michael I. Gil'
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.07.012
OpenAlex ID: W2093638956
cites work: Q5690466
cites work: Q5427954
cites work: Q3155766
cites work: Asymptotic behaviour of iterates of Volterra operators on \(L^p(0,1)\)
cites work: Mass dependence of quantum energy inequality bounds
cites work: Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
cites work: Q3857325
DOI: 10.1016/J.JMAA.2011.07.012
description: scientific article; zbMATH DE number 5962657