Parametric Poincaré-Perron theorem with applications. (English) Zbl 1236.39001
As main result the authors prove a parametric generalization of the classical Poincaré-Perron theorem [O. Perron, Math. Ann. 84, 1–15 (1921; JFM 48.0479.01)] on stabilizing recurrence relations, where the varying coefficients of the recurrence depend on auxiliary parameters and converge uniformly in these parameters to their limiting values. As an application, the authors study convergence of the ratios of families of functions satisfying finite recurrence relations with varying functional coefficients. In Section 5 of the paper, some related topics and open problems are proposed.
Reviewer: Jurang Yan (Taiyuan)
MSC:
| 39A10 | Additive difference equations |
Keywords:
parametric Poincaré-Perron theorem; recurrence relation; Poincaré difference system; asymptotic rationCitations:
JFM 48.0479.01References:
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