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Enclosure of the Numerical Range of a Class of Non-selfadjoint Rational Operator Functions
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2017 (English)In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 88, no 2, 151-184 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2017. Vol. 88, no 2, 151-184 p.
Keyword [en]
Non-linear spectral problem, Numerical range, Pseudospectra, Resolvent estimate
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-137726DOI: 10.1007/s00020-017-2378-6ISI: 000405016300001OAI: oai:DiVA.org:umu-137726DiVA: diva2:1120953
Funder
Swedish Research Council, 621-2012-3863
Available from: 2017-07-07 Created: 2017-07-07 Last updated: 2017-08-01Bibliographically approved

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Engström, ChristianTorshage, Axel
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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • de-DE
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