Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Enclosure of the Numerical Range of a Class of Non-selfadjoint Rational Operator Functions

Engström, Christian LU and Torshage, Axel (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.

Please use this url to cite or link to this publication:
author
and
publishing date
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}},
}