Boundary conditions at infinity for difference equations of limit-circle type

A second-order difference equation of limit-circle type, with parameter λ, is transformed into a first-order system. Existence and uniqueness of solutions of this system with specified limits at infinity are proved, as well as analytic dependence of the solution on the parameter λ. These results are...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 89; no. 2; pp. 442 - 461
Main Author Welstead, Stephen T
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.1982
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Summary:A second-order difference equation of limit-circle type, with parameter λ, is transformed into a first-order system. Existence and uniqueness of solutions of this system with specified limits at infinity are proved, as well as analytic dependence of the solution on the parameter λ. These results are then applied to the second-order limit-circle equation for the purpose of constructing a suitable boundary condition at infinity, and analyzing the spectrum and the resulting form of the resolvent.
ISSN:0022-247X
1096-0813
DOI:10.1016/0022-247X(82)90112-3