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Parametric Poincaré-Perron theorem with applications
Stockholm University, Faculty of Science, Department of Mathematics.
2011 (English)In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 113, no 1, 197-225 p.Article in journal (Refereed) Published
Abstract [en]

We prove a parametric generalization of the classical Poincar´e- 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 two classes of biorthogonal polynomials introduced by Ismail and Masson.

Place, publisher, year, edition, pages
2011. Vol. 113, no 1, 197-225 p.
Keyword [en]
Poincare-Perron theorem, parametric version
National Category
Mathematical Analysis
Research subject
URN: urn:nbn:se:su:diva-49759DOI: 10.1007/s11854-011-0004-0ISI: 000289562300004OAI: diva2:379384
Available from: 2010-12-31 Created: 2010-12-17 Last updated: 2012-01-20Bibliographically approved

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Shapiro, Boris
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