Gerhat, Borbala; Tretter, Christiane (2022). Pseudo Numerical Ranges and Spectral Enclosures. Complex analysis and operator theory, 16(6), p. 78. Springer 10.1007/s11785-022-01232-9
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We introduce the new concepts of pseudo numerical range for operator functions and families of sesquilinear forms as well as the pseudo block numerical range for n×n operator matrix functions. While these notions are new even in the bounded case, we cover operator polynomials with unbounded coefficients, unbounded holomorphic form families of type (a) and associated operator families of type (B). Our main results include spectral inclusion properties of pseudo numerical ranges and pseudo block numerical ranges. For diagonally dominant and off-diagonally dominant operator matrices they allow us to prove spectral enclosures in terms of the pseudo numerical ranges of Schur complements that no longer require dominance order 0 and not even <1. As an application, we establish a new type of spectral bounds for linearly damped wave equations with possibly unbounded and/or singular damping.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Gerhat, Borbala Mercedesz, Tretter, Christiane |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
1661-8262 |
Publisher: |
Springer |
Language: |
English |
Submitter: |
Zarif Ibragimov |
Date Deposited: |
15 Mar 2023 08:09 |
Last Modified: |
19 Mar 2023 02:15 |
Publisher DOI: |
10.1007/s11785-022-01232-9 |
PubMed ID: |
35789901 |
BORIS DOI: |
10.48350/180059 |
URI: |
https://boris.unibe.ch/id/eprint/180059 |
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