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title:
 
On the Spectral Theory of Operator Pencils in a Hilbert Space
publication:
 
JNMP
volume-issue:   2 - 3-4
pages:   356 - 366
ISSN:
  1402-9251
DOI:
  doi:10.2991/jnmp.1995.2.3-4.15 (how to use a DOI)
author(s):
 
Roman I. ANDRUSHKIW
publication date:
 
September 1995
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).
copyright:
 
© The authors.
This article is distributed under the terms of the Creative Commons Attribution License 4.0, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. See for details: https://creativecommons.org/licenses/by-nc/4.0/
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