On the classification of the spectrum of second order difference operators

Authors
Beckermann, B
Citation
B. Beckermann, On the classification of the spectrum of second order difference operators, MATH NACHR, 216, 2000, pp. 45-59
Citations number
13
Categorie Soggetti
Mathematics
Journal title
MATHEMATISCHE NACHRICHTEN
ISSN journal
0025584X → ACNP
Volume
216
Year of publication
2000
Pages
45 - 59
Database
ISI
SICI code
0025-584X(2000)216:<45:OTCOTS>2.0.ZU;2-O
Abstract
We study nonsymmetric second order difference operators acting in the Hilbe rt space l(2) and describe the resolvent set and the essential spectrum of such operators in terms of related formal orthogonal polynomials. As an app lication, we obtain new results on the growth of orthonormal polynomials ou tside and inside the support of the underlying measure of orthogonality.