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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A quadratic eigenvalue problem


Author: W. M. Greenlee
Journal: Proc. Amer. Math. Soc. 40 (1973), 123-127
MSC: Primary 47A70
DOI: https://doi.org/10.1090/S0002-9939-1973-0328648-7
MathSciNet review: 0328648
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Abstract: Let $ P,Q$ be compact selfadjoint operators in a Hilbert space. It is proven that the characteristic and associated vectors of the quadratic eigenvalue problem, $ x = \lambda Px + (1/\lambda )Qx$, form a Riesz basis for the cartesian product of the closure of the range of $ P$ and the closure of the range of $ Q$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0328648-7
Keywords: Quadratic eigenvalue problem, completeness, indefinite metric, Rayleigh-Taylor problem
Article copyright: © Copyright 1973 American Mathematical Society