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On a Class of Analytic Operator Functions and Their Linearizations
Author(s) -
Jonas Peter,
Trunk Carsten
Publication year - 2002
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 - 10.1002/1522-2616(200209)243:1<92::aid-mana92>3.0.co;2-q
Subject(s) - mathematics , compact operator , operator (biology) , semi elliptic operator , eigenvalues and eigenvectors , multiplication operator , finite rank operator , shift operator , quasinormal operator , pure mathematics , perturbation (astronomy) , class (philosophy) , spectrum (functional analysis) , function (biology) , mathematical analysis , differential operator , hilbert space , banach space , repressor , artificial intelligence , chemistry , computer science , biology , biochemistry , quantum mechanics , evolutionary biology , transcription factor , programming language , physics , extension (predicate logic) , gene
We consider an operator function T in a Krein space which can formally be written as (0.1)but the last term on the right of (0.1) is replaced by a relatively form‐compact perturbation of a similar form. We study relations between the operator function T , a selfadjoint operator M in some Krein space, associated with T , and an operator which can be constructed with the help of the operator function – T –1 . The results are applied to a Sturm‐Liouville problem with a coefficient depending rationally on the eigenvalue parameter.