New spectral results for the electrostatic integral operator
type: Item
instance of: scholarly article
title: New spectral results for the electrostatic integral operator
zbMATH Open document ID: 0814.47037
author: J. F. Ahner
author: V. V. Dyakin
author: V. Ya. Raevskii
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-06-12T00:00:00Z
review text: Two new fundamental results are established concerning the spectra of both the double-layer potential and the electrostatic integral operators in \(\mathbb{R}^ 3\). While it is known that 0 lies in the spectrum of each operator, its specific nature is not well understood. For some geometries (e.g., a sphere and a prolate spheroid), it is known that 0 lies in their continuous spectra. In this paper, the authors produce specific examples, where 0 lies in the point spectrum of each operator. Thus it is established that the spectral nature of 0 depends upon the geometry of the underlying surface. The second new result given is an important generalization of a recent paper concerning the possible refinement of a classical result of Plemelj.
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 78A30
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 663695
zbMATH Keywords: double-layer potential
zbMATH Keywords: electrostatic integral operators
zbMATH Keywords: point spectrum
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1257
OpenAlex ID: W2015884716
DOI: 10.1006/JMAA.1994.1257
description: scientific article; zbMATH DE number 663695