Abstract
Self-adjoint quadratic operator pencilsL(λ)=λ 2 A + λB + C with a noninvertible leading operatorA are considered. In particular, a characterization of the spectral points of positive and of negative type ofL is given, and their behavior under a compact perturbation is studied. These results are applied to a pencil arising in magnetohydrodynamics.
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Adamjan, V., Langer, H. & Möller, M. Compact perturbation of definite type spectra of self-adjoint quadratic operator pencils. Integr equ oper theory 39, 127–152 (2001). https://doi.org/10.1007/BF01195813
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DOI: https://doi.org/10.1007/BF01195813