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Square Powers of Singularly Perturbed Operators
Author(s) -
Albeverio Sergio,
Karwowski Witold,
Koshmanenko Vladimir
Publication year - 1995
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.19951730102
Subject(s) - mathematics , self adjoint operator , hilbert space , operator (biology) , perturbation (astronomy) , singular perturbation , singular solution , strictly singular operator , square (algebra) , hermitian adjoint , quasinormal operator , singular value , pure mathematics , mathematical analysis , finite rank operator , eigenvalues and eigenvectors , banach space , geometry , quantum mechanics , biochemistry , chemistry , physics , repressor , transcription factor , gene
We use the method of self‐adjoint extensions to define a self‐adjoint operator A T as the singular perturbation of a given self‐adjoint operator A by a singular operator T on a Hilbert space. We also find the structure of a singular operator Q such that the singular perturbation of A 2 by Q satisfies ( A 2 ) Q = ( A T ) 2 . We obtain the explicit form of Q in terms of A and T . A definition of the n ‐th power for strictly positive symmetric operators is also given.
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