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On the point spectrum of ℋ︁ –2 ‐singular perturbations
Author(s) -
Albeverio Sergio,
Dudkin Mykola,
Konstantinov Alexei,
Koshmanenko Volodymyr
Publication year - 2007
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.200410461
Subject(s) - mathematics , orthonormal basis , countable set , hilbert space , eigenvalues and eigenvectors , operator (biology) , spectrum (functional analysis) , separable space , space (punctuation) , pure mathematics , set (abstract data type) , mathematical analysis , combinatorics , discrete mathematics , biochemistry , chemistry , physics , linguistics , philosophy , repressor , quantum mechanics , computer science , transcription factor , gene , programming language
Abstract We prove that for any self‐adjoint operator A in a separable Hilbert space ℋ and a given countable set Λ = { λ i } i ∈ℕ of real numbers, there exist ℋ –2 ‐singular perturbations à of A such that Λ ⊂ σ p ( à ). In particular, if Λ = { λ 1 ,…, λ n } is finite, then the operator à solving the eigenvalues problem, à ψ k = λ k ψ k , k = 1,…, n , is uniquely defined by a given set of orthonormal vectors { ψ k } nk =1 satisfying the condition span { ψ k } nk =1 ∩ dom (| A | 1/2 ) = {0}. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)