Premium
On the Classification of the Spectrum of Second Order Difference Operators
Author(s) -
Beckermann Bernhard
Publication year - 2000
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(200008)216:1<45::aid-mana45>3.0.co;2-r
Subject(s) - mathematics , orthogonality , hilbert space , orthonormal basis , spectrum (functional analysis) , order (exchange) , resolvent , orthogonal polynomials , pure mathematics , set (abstract data type) , operator (biology) , algebra over a field , space (punctuation) , biochemistry , chemistry , physics , geometry , linguistics , philosophy , finance , repressor , quantum mechanics , computer science , transcription factor , economics , gene , programming language
We study nonsymmetric second order difference operators acting in the Hilbert space 2 and describe the resolvent set and the essential spectrum of such operators in terms of related formal orthogonal polynomials. As an application, we obtain new results on the growth of orthonormal polynomials outside and inside the support of the underlying measure of orthogonality.