On the Existence of WKB‐Type Asymptotics for the Generalized Eigenvectors of Discrete String Operators | Zendy

Belov Sergei | Zendy; Rybkin Alexei | Zendy

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On the Existence of WKB‐Type Asymptotics for the Generalized Eigenvectors of Discrete String Operators

Author(s) -

Belov Sergei,

Rybkin Alexei

Publication year - 2004

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/s0024609303002819

Subject(s) - mathematics , wkb approximation , eigenvalues and eigenvectors , type (biology) , bounded function , diagonal , string (physics) , diagonal matrix , zero (linguistics) , pure mathematics , matrix (chemical analysis) , mathematical analysis , combinatorics , mathematical physics , quantum mechanics , physics , geometry , ecology , linguistics , philosophy , materials science , composite material , biology

Let J be a Jacobi real symmetric matrix on l 2 with zero diagonal and non‐diagonal entries of the form {1 + p n }. If p n −1 ± p n = O ( n −α ) with some α2/3, then the existence of bounded solutions of Ju = λ u is proved for almost every λ ∈ (−2, 2) with the WKB‐type asymptotic behavior. 2000 Mathematics Subject Classification 47B36, 47B37, 47B39.

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