Enclosure of the Numerical Range of a Class of Non-selfadjoint Rational Operator Functions
(2017) In Integral Equations and Operator Theory 88(2). p.151-184- Abstract
In this paper we introduce an enclosure of the numerical range of a class of rational operator functions. In contrast to the numerical range the presented enclosure can be computed exactly in the infinite dimensional case as well as in the finite dimensional case. Moreover, the new enclosure is minimal given only the numerical ranges of the operator coefficients and many characteristics of the numerical range can be obtained by investigating the enclosure. We introduce a pseudonumerical range and study an enclosure of this set. This enclosure provides a computable upper bound of the norm of the resolvent.
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https://lup.lub.lu.se/record/9b209158-34c0-4129-b10f-83dbb9454b5c
- author
- Engström, Christian LU and Torshage, Axel
- publishing date
- 2017-06-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Non-linear spectral problem, Numerical range, Pseudospectra, Resolvent estimate
- in
- Integral Equations and Operator Theory
- volume
- 88
- issue
- 2
- pages
- 34 pages
- publisher
- Springer
- external identifiers
-
- scopus:85019943472
- ISSN
- 0378-620X
- DOI
- 10.1007/s00020-017-2378-6
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2017, The Author(s).
- id
- 9b209158-34c0-4129-b10f-83dbb9454b5c
- date added to LUP
- 2023-03-24 11:08:30
- date last changed
- 2023-03-24 13:55:49
@article{9b209158-34c0-4129-b10f-83dbb9454b5c, abstract = {{<p>In this paper we introduce an enclosure of the numerical range of a class of rational operator functions. In contrast to the numerical range the presented enclosure can be computed exactly in the infinite dimensional case as well as in the finite dimensional case. Moreover, the new enclosure is minimal given only the numerical ranges of the operator coefficients and many characteristics of the numerical range can be obtained by investigating the enclosure. We introduce a pseudonumerical range and study an enclosure of this set. This enclosure provides a computable upper bound of the norm of the resolvent.</p>}}, author = {{Engström, Christian and Torshage, Axel}}, issn = {{0378-620X}}, keywords = {{Non-linear spectral problem; Numerical range; Pseudospectra; Resolvent estimate}}, language = {{eng}}, month = {{06}}, number = {{2}}, pages = {{151--184}}, publisher = {{Springer}}, series = {{Integral Equations and Operator Theory}}, title = {{Enclosure of the Numerical Range of a Class of Non-selfadjoint Rational Operator Functions}}, url = {{http://dx.doi.org/10.1007/s00020-017-2378-6}}, doi = {{10.1007/s00020-017-2378-6}}, volume = {{88}}, year = {{2017}}, }