Orthogonal structure on a wedge and on the boundary of a square
Classical Analysis and ODEs
2018-07-06 v2 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.1710.08654,
title = {Orthogonal structure on a wedge and on the boundary of a square},
author = {Sheehan Olver and Yuan Xu},
journal= {arXiv preprint arXiv:1710.08654},
year = {2018}
}
Comments
to appear in FoCM