Orthogonal structure on a wedge and on the boundary of a square

2017/10/24 by Sheehan Olver, Yuan Xu, Olver, Sheehan +1 · 1 citation
Mathematics · Physics and Astronomy · #Mathematical functions and polynomials #Random Matrices and Applications #Advanced Mathematical Theories and Applications

paper · pdf · doi:10.48550/arxiv.1710.08654

Abstract

Orthogonal polynomials with respect to a weight function defined on a wedge in the plane are studied. A basis of orthogonal polynomials is explicitly constructed for two large class of weight functions and the convergence of Fourier orthogonal expansions is studied. These are used to establish analogous results for orthogonal polynomials on the boundary of the square. As an application, we study the statistics of the associated determinantal point process and use the basis to calculate Stieltjes transforms.

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• Elliptic orthogonal polynomials and OPRL

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