Enclosure of the numerical range of a class of non-selfadjoint rational operator functions

Engström, Christian; Torshage, Johan Axel (2017). Enclosure of the numerical range of a class of non-selfadjoint rational operator functions. Integral equations and operator theory, 88(2), pp. 151-184. Birkhäuser 10.1007/s00020-017-2378-6

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Torshage, Johan Axel

Subjects:

500 Science > 510 Mathematics

ISSN:

0378-620X

Publisher:

Birkhäuser

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

05 Sep 2019 15:54

Last Modified:

24 Oct 2019 19:44

Publisher DOI:

10.1007/s00020-017-2378-6

BORIS DOI:

10.7892/boris.125534

URI:

https://boris.unibe.ch/id/eprint/125534

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