A note on asymptotic zero distribution of orthogonal polynomials

Zero Asymptotic Behaviour for Orthogonal Matrix Polynomials

Weak-star asymptotic results are obtained for the zeros of orthogonal matrix polynomials (i.e. the zeros of their determinants) on R from two di®erent assumptions: ̄rst from the convergence of matrix coe±cients occurring in the three-term recurrence for these polynomials and, second, from some conditions on the generating matrix measure. The matrix analogue of the Chebyshev polynomials of the ̄...

Asymptotic zero distribution of biorthogonal polynomials

Let ψ : [0, 1] → R be a strictly increasing continuous function. Let Pn be a polynomial of degree n determined by the biorthogonality conditions ∫ 1 0 Pn (x)ψ (x) j dx = 0, j = 0, 1, . . . , n− 1. We study the distribution of zeros of Pn as n → ∞, and related potential theory.

Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature

In this paper we study the asymptotic behavior of a family of polynomials which are orthogonal with respect to an exponential weight on certain contours of the complex plane. The zeros of these polynomials are the nodes for complex Gaussian quadrature of an oscillatory integral on the real axis with a high order stationary point, and their limit distribution is also analyzed. We show that the z...

Asymptotic Zero Distribution of Orthogonal Polynomials with Discontinuously Varying Recurrence Coefficients

The zero distribution of orthogonal polynomials pn,N , n = 0, 1, . . . generated by recurrence coefficients an,N and bn,N depending on a parameter N has been recently considered by Kuijlaars and Van Assche under the assumption that an,N and bn,N behave like a(n/N) and b(n/N), respectively, where a(·) and b(·) are continuous functions. Here, we extend this result by allowing a(·) and b(·) to be ...

Note on Certain Orthogonal Polynomials