Abstract
In Chapter 15, we studied the question of the stability of a discrete eigenvalue λ0 of an operator T 0 under an analytic perturbation T k. The main result, Theorem 15.11, states that the family T k, for k in a small complex neighborhood of 0, will have eigenvalues near λ0 of total algebraic multiplicity equal to that of λ0. This is what we mean by the stability of λ0 with respect to the familyT 0. With regard to the perturbation theory of discrete eigenvalues, this theorem is quite satisfactory.
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© 1996 Springer Science+Business Media New York
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Hislop, P.D., Sigal, I.M. (1996). The General Theory of Spectral Stability. In: Introduction to Spectral Theory. Applied Mathematical Sciences, vol 113. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0741-2_19
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DOI: https://doi.org/10.1007/978-1-4612-0741-2_19
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6888-8
Online ISBN: 978-1-4612-0741-2
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