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A variational principle in Kreĭn space


Authors: Paul Binding and Branko Najman
Journal: Trans. Amer. Math. Soc. 342 (1994), 489-499
MSC: Primary 47B50; Secondary 47A75, 49R10
DOI: https://doi.org/10.1090/S0002-9947-1994-1181181-3
MathSciNet review: 1181181
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Abstract: A variational characterization, involving a max-inf of the Rayleigh quotient, is established for certain eigenvalues of a wide class of definitizable selfadjoint operators Q in a Krein space. The operator Q may have continuous spectrum and nonreal and nonsemisimple eigenvalues; in particular it may have embedded eigenvalues. Various applications are given to selfadjoint linear and quadratic eigenvalue problems with weak definiteness assumptions.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1994-1181181-3
Keywords: Minimax principle for eigenvalues, selfadjoint operators in Krein space, spectral functions, elliptic problems with indefinite weight
Article copyright: © Copyright 1994 American Mathematical Society

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