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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Published in | Journal of mathematical analysis and applications Vol. 89; no. 2; pp. 442 - 461 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.01.1982
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Online Access | Get full text |
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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. |
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ISSN: | 0022-247X 1096-0813 |
DOI: | 10.1016/0022-247X(82)90112-3 |