Orthogonal Structure on a Wedge and on the Boundary of a Square
Orthogonal Structure on a Wedge and on the Boundary of a Square
复制标题
楔形和正方形边界上的正交结构
DOI：
--
复制
发表时间：
2017
影响因子：
3
通讯作者：
Yuan Xu
中科院分区：
文献类型：
--
作者：
S. Olver;Yuan Xu
研究了平面上楔形体上权函数的正交多项式。对两大类权函数构造了一组正交多项式基，并研究了Fourier正交展开式的收敛性。这些都是用来建立类似的结果正交多项式的边界上的平方。作为应用，我们研究了相关的行列式点过程的统计特性，并利用该基计算了Stieltjes变换。
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.