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

We give a lower bound for solutions of linear recurrence relations of the form zan = ∑n+Nk=n−N αk, nak, whenever z is not in the lp-spectrum of the corresponding banded operator. In particular if Pn, are polynomials orthonormal with respect to a measure μ supported in a bounded interval the sequence Pn(x)2 + Pn+1(x)2 is bounded from below by (1 + ϵ)n, for x ∉ supp μ. We give an application to polynomial hypergroups.