Fe b 20 09 Uniform Asymptotics of the Meixner Polynomials

Uniform Asymptotics of the Meixner Polynomials

Using the Deift-Zhou steepest descent method, we derive locally uniform asymptotic formulas for the Meixner polynomials. So far as we know, the asymptotic behavior in a neighborhood of the origin has not been studied before. To fill this gap, we should impose a Cauchy integral, which is the uniformly bounded solution to a scalar Riemann-Hilbert problem, and which converges exponentially fast (a...

Se p 20 09 MEIXNER POLYNOMIALS OF THE SECOND KIND AND QUANTUM ALGEBRAS REPRESENTING

We show how Viennot’s combinatorial theory of orthogonal polynomials may be used to generalize some recent results of Sukumar and Hodges on the matrix entries in powers of certain operators in a representation of su(1, 1). Our results link these calculations to finding the moments and inverse polynomial coefficients of certain Laguerre polynomials and Meixner polynomials of the second kind. As ...

Global asymptotics of the Meixner polynomials

ar X iv : 0 90 2 . 15 71 v 1 [ m at h . SP ] 1 0 Fe b 20 09 RIGHT LIMITS AND REFLECTIONLESS MEASURES FOR CMV MATRICES

We study CMV matrices by focusing on their right-limit sets. We prove a CMV version of a recent result of Remling dealing with the implications of the existence of absolutely continuous spectrum, and we study some of its consequences. We further demonstrate the usefulness of right limits in the study of weak asymptotic convergence of spectral measures and ratio asymptotics for orthogonal polyno...

Asymptotics of Derivatives of Orthogonal Polynomials on the Real Line

We show that uniform asymptotics of orthogonal polynomials on the real line imply uniform asymptotics for all their derivatives. This is more technically challenging than the corresponding problem on the unit circle. We also examine asymptotics in the L2 norm. 1. Results Let μ be a nite positive Borel measure on [−1, 1] and let {pn}n=0 denote the corresponding orthonormal polynomials, so that ∫...