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Asymptotics of orthogonal polynomials with respect to an analytic weight with algebraic singularities on the circle

- A. Martínez-Finkelshtein, K. Mclaughlin, E. Saff
- Mathematics
- 29 May 2006

Strong asymptotics of polynomials orthogonal on the unit circle with respect to a weight of the form

Szego Orthogonal Polynomials with Respect to an Analytic Weight: Canonical Representation and Strong Asymptotics

- A. Martínez-Finkelshtein, K. Mclaughlin, E. Saff
- Mathematics
- 15 February 2005

AbstractWe provide a representation in terms of certain canonical functions
for a sequence of polynomials orthogonal with respect to a weight
that is strictly positive and analytic on the unit… Expand

Non-Intersecting Squared Bessel Paths: Critical Time and Double Scaling Limit

- A. Kuijlaars, A. Martínez-Finkelshtein, F. Wielonsky
- Mathematics
- 4 November 2010

AbstractWe consider the double scaling limit for a model of n non-intersecting squared Bessel processes in the confluent case:
all paths start at time t = 0 at the same positive value x = a, remain… Expand

Asymptotic Properties of Heine-Stieltjes and Van Vleck Polynomials

- A. Martínez-Finkelshtein, E. Saff
- MathematicsJ. Approx. Theory
- 1 September 2002

We study the asymptotic behavior of the zeros of polynomial solutions of a class of generalized Lam? differential equations, when their coefficients satisfy certain asymptotic conditions. The limit… Expand

Asymptotic properties of Sobolev orthogonal polynomials

- A. Martínez-Finkelshtein
- Mathematics
- 16 November 1998

Orthogonality of Jacobi polynomials with general parameters

- A. Kuijlaars, A. Martínez-Finkelshtein, R. Orive
- Mathematics
- 6 January 2003

In this paper we study the orthogonality conditions satisfied by Jacobi polynomials $P_n^{(\alpha,\beta)}$ when the parameters $\alpha$ and $\beta$ are not necessarily $>-1$. We establish… Expand

Critical Measures, Quadratic Differentials, and Weak Limits of Zeros of Stieltjes Polynomials

- A. Martínez-Finkelshtein, E. Rakhmanov
- Mathematics
- 2 February 2009

We investigate the asymptotic zero distribution of Heine-Stieltjes polynomials – polynomial solutions of second order differential equations with complex polynomial coefficients. In the case when all… Expand

Analytic aspects of Sobolev orthogonal polynomials revisited

- A. Martínez-Finkelshtein
- Mathematics
- 15 January 2001

Asymptotics for Minimal Discrete Riesz Energy on Curves in ℝ d

- A. Martínez-Finkelshtein, V. Maymeskul, E. A. Rakhmanov, E. Saff
- MathematicsCanadian Journal of Mathematics
- 1 June 2004

Abstract We consider the $s$ -energy $E({{Z}_{n}};\,s)={{\Sigma }_{i\ne j}}K(\parallel {{z}_{i,n}}\,-\,{{z}_{j,n}}\parallel \,;\,s)$ for point sets $Zn\,=\,\{{{z}_{k,n}}\,:\,k\,=\,0,\,\ldots \,,\,n\}… Expand

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