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Orthogonal polynomials with respect to a weight function defined on a wedgein the plane are studied. A basis of orthogonal polynomials is explicitlyconstructed for two large class of weight functions and the convergence ofFourier orthogonal expansions is studied. These are used to establish analogousresults for orthogonal polynomials on the boundary of the square. As anapplication, we study the statistics of the associated determinantal pointprocess and use the basis to calculate Stieltjes transforms.

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