Averages of Ratios of Christoffel Functions for Compactly Supported Measures

Collocation Method using Compactly Supported Radial Basis Function for Solving Volterra's Population Model

‎In this paper‎, ‎indirect collocation approach based on compactly supported radial basis function (CSRBF) is applied for solving Volterra's population model. The method reduces the solution of this problem to the solution of a system of algebraic equations‎. ‎Volterra's model is a non-linear integro-differential equation where the integral term represents the effect of toxin‎. ‎To solve the pr...

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

On Christoffel Functions and Related Quantities for Compactly Supported Measures

Let be a compactly supported positive measure on the real line, with associated orthogonal polynomials fpng. Without any global restrictions such as regularity, we discuss convergence in measure for (i) ratio asymptotics for Christo¤el functions; (ii) the Nevai operators (aka the Nevai condition); (iii) universality limits in the bulk. We also establish convergence a.e. for su¢ cently sparse su...

A Variational Principle for Correlation Functions for Unitary Ensembles, with Applications

In the theory of random matrices for unitary ensembles associated with Hermitian matrices,m−point correlation functions play an important role. We show that they possess a useful variational principle. Let μ be a measure with support in the real line, and Kn be the nth reproducing kernel for the associated orthonormal polynomials. We prove that for m ≥ 1, det [Kn (μ, xi, xj)]1≤1,j≤m = m! sup P ...

Bernstein–Szegő polynomials on the triangle

In this work we consider the extension of the one variable Bernstein–Szegő theory for orthogonal polynomials on the real line (see [3]) to bivariate measures supported on the triangle. A similar problem for measures supported in the square was studied in [1]. Following essentially [2] the orthogonal polynomials and the corresponding kernel functions are constructed. Finally, some asymptotic res...