Strongly definitizable linear pencils in Hilbert space |
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| Authors: | P Lancaster A Shkalikov Qiang Ye |
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| Institution: | (1) Department of Mathematics & Statistics, The University of Calgary, T2N 1N4 Calgary, Alberta, Canada;(2) Department of Mathematics, Moscow State University, Moscow, Russia;(3) Department of Applied Mathematics, The University of Manitoba, R3T 2N2 Winnipeg, Manitoba, Canada |
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| Abstract: | Selfadjoint linear pencils  F–G are considered which have discrete spectrum and neither F nor G is definite. Several characterizations are given of a  strongly definitizable property when F and G are bounded, and also when both operators are unbounded. The theory is applied to analysis of the stability of a linear second order initial-boundary value problem with boundary conditions dependent on the eigenvalue parameter.Research supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada. |
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| Keywords: | 47A70 47E05 |
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