A spectral property of the electrostatic integral operator
type: Item
instance of: scholarly article
title: A spectral property of the electrostatic integral operator
zbMATH Open document ID: 0939.45001
author: Erich Martensen
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-07-05T00:00:00Z
review text: Integral operators in general and of the electrostatic type in particular, play a prominent role in mathematical analyses and applications. The author here is concerned with the eigenvalue problems for the electrostatic and adjoint electrostatic integral operators: \[ T,T': C(E)\to C(E) \] defined by means of appropriate integral equations. After stating and proving a preparatory lemma on spherical harmonics, a conjecture on the sum of eigenvalues belonging to \(2n+1\) linearly independent eigenfunctions (lief) is given and discussed. The spectral property is examined at length. It is shown that the arithmetic means of the eigenvalues corresponding to the maximum number of liefs of equal order is the same for the ellipsoid as for the sphere. The work can serve as a practical tool for the determination of ellipsoidal harmonics and issues thereof.
Mathematics Subject Classification ID: 45C05
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 78A30
zbMATH DE Number: 1375015
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: electrostatic integral operators
zbMATH Keywords: spherical harmonics
zbMATH Keywords: eigenfunctions
zbMATH Keywords: ellipsoidal harmonics
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6538
OpenAlex ID: W1989674136
cites work: On the eigenvalues of the electrostatic integral operator. II
cites work: On the eigenvalues of the electrostatic integral operator
cites work: New spectral results for the electrostatic integral operator
cites work: Attacking a conjecture in mathematical physics by combining methods of computational analysis and scientific computing
cites work: Q4481373
cites work: Q5823489
cites work: Q4855520
cites work: Q4763640
cites work: A sum-property of the eigenvalues of the electrostatic integral operator
DOI: 10.1006/JMAA.1999.6538
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description: scientific article; zbMATH DE number 1375015