Dilatation and the asymptotics of the eigenvalues of spectral problems with singularities
type: Item
instance of: scholarly article
title: Dilatation and the asymptotics of the eigenvalues of spectral problems with singularities
zbMATH Open document ID: 0628.35077
DOI: 10.1007/BF01083493
author: S. I. Fedorova
author: Victor Ivrii
publication date: 1986-01-01T00:00:00Z
review text: The eigenvalue problem \(Au=\lambda^ 2\mu u\) is investigated providing that A is a uniformly elliptic selfadjoint operator of the 2nd order and \(\mu\) is a nonnegative weight function. The term singularity means either the nonregularity of \(\mu\) or of the coefficients of A, degeneration of \(\mu\), unboundedness of the domain or nonregularity of the boundary. It is shown how the method of dilatations facilitates to derive very precise asymptotics of eigenvalues of the spectral problem with sufficiently weak singularities.
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 47A70
zbMATH DE Number: 4021768
zbMATH Keywords: uniformly elliptic
zbMATH Keywords: selfadjoint operator
zbMATH Keywords: method of dilatations
zbMATH Keywords: asymptotics of eigenvalues
zbMATH Keywords: weak singularities
MaRDI profile type: Publication
cites work: The spectral function of an elliptic operator
cites work: Spectrum and its distribution function for a transversally elliptic operator
cites work: Q3897569
full work available at URL: https://doi.org/10.1007/bf01083493
OpenAlex ID: W2092937489
published in: Functional Analysis and Its Applications
Recommended article: Q4846328
Recommended article: Asymptotics of eigenvalues for Sturm-Liouville problems with an interior singularity
Recommended article: Asymptotics of the eigenvalues of a boundary value problem for a vector singular differential equation
Recommended article: Q3805325
Recommended article: Asymptotic expansion of eigenvalues of the Laplace operator in domains with singularly perturbed boundary
Recommended article: Q4383307
Recommended article: Q3022510
Recommended article: Eigenvalue asymptotics for Sturm--Liouville operators with singular potentials
Recommended article: Asymptotic of singular numbers and eigenvalues of weakly perturbed operators
Recommended article: Asymptotic expansions for eigenvalues of the Steklov problem in singularly perturbed domains
description: scientific article; zbMATH DE number 4021768