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On the perturbation theory of instable isolated eigenvalues
Author(s) -
Demuth M.
Publication year - 1974
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19740640122
Subject(s) - eigenvalues and eigenvectors , mathematics , perturbation (astronomy) , eigenvalue perturbation , poincaré–lindstedt method , embedding , mathematical analysis , singular perturbation , mathematical physics , quantum mechanics , physics , artificial intelligence , computer science
The problem of the perturbation of an operator having a continuous spectrum and an isolated eigenvalue λ 0 is considered by means of the theory on embedded eigenvalues. The perturbation is divided up into two parts. One part is used for embedding the isolated eigenvalue λ 0 . This embedded eigenvalue becomes instable by the second part of the perturbation and spectral concentration is given near λ 0 . The general model is illustrated by a simple example.