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Abstract
For a very general class of unbounded self-adjoint operator function we prove upper bounds for eigenvalues which lie within arbitrary gaps of the essential spectrum. These upper bounds are given by triple variations. Furthermore, we find conditions which imply that a point is in the resolvent set. For norm resolvent continuous operator functions we show that the variational inequality becomes an equality.
Original language | English |
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Pages (from-to) | 2019-2047 |
Number of pages | 29 |
Journal | Journal of Functional Analysis |
Volume | 270 |
Issue number | 6 |
Early online date | 19 Jan 2016 |
DOIs | |
Publication status | Published - 15 Mar 2016 |
Keywords
- variational principles for eigenvalues
- operator function
- spectral decomposition
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Dive into the research topics of 'Triple variational principles for self-adjoint operator functions'. Together they form a unique fingerprint.Profiles
Projects
- 1 Finished
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Spectral Theory of Block Operator Matrices
Langer, M. (Principal Investigator)
EPSRC (Engineering and Physical Sciences Research Council)
1/09/07 → 30/11/09
Project: Research