Accumulation of complex eigenvalues of a class of analytic operator functions
(2018) In Journal of Functional Analysis 275(2). p.442-477- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/91cd90c8-5300-471f-9f54-75ed6e8aba0e
- author
- Engström, Christian LU and Torshage, Axel
- publishing date
- 2018-07-15
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Non-linear spectral problem, Numerical range, Operator pencil, Spectral divisor
- in
- Journal of Functional Analysis
- volume
- 275
- issue
- 2
- pages
- 36 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85045081595
- ISSN
- 0022-1236
- DOI
- 10.1016/j.jfa.2018.03.019
- language
- English
- LU publication?
- no
- additional info
- Funding Information: The authors gratefully acknowledge the support of the Swedish Research Council under Grant No. 621-2012-3863 . Publisher Copyright: © 2018 Elsevier Inc.
- id
- 91cd90c8-5300-471f-9f54-75ed6e8aba0e
- date added to LUP
- 2023-03-24 11:06:31
- date last changed
- 2023-03-24 13:44:14
@article{91cd90c8-5300-471f-9f54-75ed6e8aba0e,
abstract = {{<p>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.</p>}},
author = {{Engström, Christian and Torshage, Axel}},
issn = {{0022-1236}},
keywords = {{Non-linear spectral problem; Numerical range; Operator pencil; Spectral divisor}},
language = {{eng}},
month = {{07}},
number = {{2}},
pages = {{442--477}},
publisher = {{Elsevier}},
series = {{Journal of Functional Analysis}},
title = {{Accumulation of complex eigenvalues of a class of analytic operator functions}},
url = {{http://dx.doi.org/10.1016/j.jfa.2018.03.019}},
doi = {{10.1016/j.jfa.2018.03.019}},
volume = {{275}},
year = {{2018}},
}