Parrametric Poincare-Perron theorem with applications

Details Parrametric Poincare-Perron theorem with applications Parrametric Poincare-Perron theorem with applications

2009-09-07

arxiv.org/abs/0909.1216v2

Mathematics

Functional Analysis

22 pages, 4 figures, substantially revised final version, to appear in Journal d'Analyse Mathematique

Scientific paper

We prove a parametric generalization of the classical Poincare-Perron theorem on stabilizing recurrence relations where we assume that the varying coefficients of a recurrence depend on auxiliary parameters and converge uniformly in these parameters to their limiting values. As an application we study convergence of the ratios of families of functions satisfying finite recurrence relations with varying functional coefficients. For example, we explicitly describe the asymptotic ratio for sequences of biorthogonal polynomials introduced by Ismail and Masson.

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