umu.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Enclosure of the Numerical Range and Resolvent Estimates of Non-Selfadjoint Operator Functions
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
(English)Manuscript (preprint) (Other academic)
Keywords [en]
Non-linear spectral problem, numerical range, joint numerical range, pseudospectrum, resolvent estimate
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-143084OAI: oai:DiVA.org:umu-143084DiVA, id: diva2:1166499
Available from: 2017-12-15 Created: 2017-12-15 Last updated: 2018-06-09
In thesis
1. Non-selfadjoint operator functions
Open this publication in new window or tab >>Non-selfadjoint operator functions
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Spectral properties of linear operators and operator functions can be used to analyze models in nature. When dispersion and damping are taken into account, the dependence of the spectral parameter is in general non-linear and the operators are not selfadjoint.

In this thesis non-selfadjoint operator functions are studied and several methods for obtaining properties of unbounded non-selfadjoint operator functions are presented. Equivalence is used to characterize operator functions since two equivalent operators share many significant characteristics such as the spectrum and closeness. Methods of linearization and other types of equivalences are presented for a class of unbounded operator matrix functions.

To study properties of the spectrum for non-selfadjoint operator functions, the numerical range is a powerful tool. The thesis introduces an optimal enclosure of the numerical range of a class of unbounded operator functions. The new enclosure can be computed explicitly, and it is investigated in detail. Many properties of the numerical range such as the number of components can be deduced from the enclosure. Furthermore, it is utilized to prove the existence of an infinite number of eigenvalues accumulating to specific points in the complex plane. Among the results are proofs of accumulation of eigenvalues to the singularities of a class of unbounded rational operator functions. The enclosure of the numerical range is also used to find optimal and computable estimates of the norm of resolvent and a corresponding enclosure of the ε-pseudospectrum. 

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2017. p. 21
Series
Research report in mathematics, ISSN 1653-0810 ; 60
Keywords
Non-linear spectral problem, numerical range, pseudospectrum, resolvent estimate, equivalence after extension, block operator matrices, operator functions, operator pencil, spectral divisor, joint numerical range
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-143085 (URN)978-91-7601-787-6 (ISBN)
Public defence
2018-01-19, MA 121, MIT-huset, Umeå, 09:00 (English)
Opponent
Supervisors
Available from: 2017-12-20 Created: 2017-12-15 Last updated: 2018-06-09Bibliographically approved

Open Access in DiVA

No full text in DiVA

Authority records BETA

Torshage, Axel

Search in DiVA

By author/editor
Torshage, Axel
By organisation
Department of Mathematics and Mathematical Statistics
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 32 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf