Journal of Nonlinear Mathematical Physics

Volume 2, Issue 3-4, September 1995, Pages 356 - 366

On the Spectral Theory of Operator Pencils in a Hilbert Space

Authors
Roman I. ANDRUSHKIW
Corresponding Author
Roman I. ANDRUSHKIW
Available Online 19 December 2006.
DOI
https://doi.org/10.2991/jnmp.1995.2.3-4.15How to use a DOI?
Abstract
Consider the operator pencil L = A - B - 2 C, where A, B, and C are linear, in general unbounded and nonsymmetric, operators densely defined in a Hilbert space H. Sufficient conditions for the existence of the eigenvalues of L are investigated in the case when A, B and C are K-positive and K-symmetric operators in H, and a method to bracket the eigenvalues of L is developed by using a variational characterization of the problem (i) Lu = 0. The method generates a sequence of lower and upper bounds converging to the eigenvalues of L and can be considered an extension of the Temple-Lehman method to quadratic eigenvalue problems (i).
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
2 - 3
Pages
356 - 366
Publication Date
2006/12
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1995.2.3-4.15How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Roman I. ANDRUSHKIW
PY  - 2006
DA  - 2006/12
TI  - On the Spectral Theory of Operator Pencils in a Hilbert Space
JO  - Journal of Nonlinear Mathematical Physics
SP  - 356
EP  - 366
VL  - 2
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1995.2.3-4.15
DO  - https://doi.org/10.2991/jnmp.1995.2.3-4.15
ID  - ANDRUSHKIW2006
ER  -