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Spectral Analysis of Non‐Selfadjoint Discrete Schrödinger Operators with Spectral Singularities
Author(s) -
Krall Allan M.,
Bairamov Elgiz,
Cakar Oner
Publication year - 2001
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(200111)231:1<89::aid-mana89>3.0.co;2-y
Subject(s) - mathematics , gravitational singularity , operator (biology) , cauchy distribution , pure mathematics , mathematical analysis , function (biology) , representation (politics) , spectral properties , mathematical physics , type (biology) , sequence (biology) , boundary (topology) , physics , astrophysics , ecology , biochemistry , chemistry , genetics , repressor , evolutionary biology , biology , politics , political science , transcription factor , law , gene
Let L denote the non‐selfadjoint discrete Schrödinger operator generated in 2 (ℕ) by the difference expression ( y ) n = y n –1 + y n + 1 + b n y n , n ∈ ℕ = {1, 2, …,} and the boundary condition y 0 = 0, where { b n } ∞ n = 1 is a complex sequence. In this paper we investigate Weyl‐Titchmarsh ( W – T ) function of the operator L and obtained the relation between W – T function and the generalized spectral function of L in the sense of Marchenko . Moreover we find Cauchy type integral representation of W – T function. Using this representation we derived the spectral expansion of L in terms of the principal vectors, taking into account the spectral singularities.