Accumulation of Complex Eigenvalues of a Class of Analytic Operator Functions
Functional Analysis
2018-04-05 v2
Abstract
For analytic operator functions, we prove accumulation of branches of complex eigenvalues to the essential spectrum. Moreover, we show minimality and completeness of the corresponding system of eigenvectors and associated vectors. These results are used to prove sufficient conditions for eigenvalue accumulation to the poles and to infinity of rational operator functions. Finally, an application of electromagnetic field theory is given.
Keywords
Cite
@article{arxiv.1709.01462,
title = {Accumulation of Complex Eigenvalues of a Class of Analytic Operator Functions},
author = {Christian Engström and Axel Torshage},
journal= {arXiv preprint arXiv:1709.01462},
year = {2018}
}
Comments
31 pages, 4 figures