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A Lower Bound for Orthogonal Polynomials with an Application to Polynomial Hypergroups

✍ Scribed by R. Szwarc

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 173 KB
Volume: 81
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1995.1040

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✦ Synopsis

We give a lower bound for solutions of linear recurrence relations of the form (z a_{n}=\sum_{k=n-N}^{n+N} \alpha_{k, n} a_{k}), whenever (z) is not in the (P^{P})-spectrum of the corresponding banded operator. In particular if (P_{n}) are polynomials orthonormal with respect to a measure (\mu) supported in a bounded interval the sequence (P_{n}(x)^{2}+P_{n+1}(x)^{2}) is bounded from below by ((1+\varepsilon)^{n}), for (x \notin \operatorname{supp} \mu). We give an application to polynomial hypergroups. 1995 Academic Press, Inc.

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