Orthogonal Polynomials and Fourier Orthogonal Series on a Cone
Orthogonal Polynomials and Fourier Orthogonal Series on a Cone
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锥体上的正交多项式和傅里叶正交级数
DOI：
10.1007/s00041-020-09741-x
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发表时间：
2019
影响因子：
1.2
通讯作者：
Yuan Xu
中科院分区：
文献类型：
--
作者：
Yuan Xu
研究了锥上的正交多项式和傅里叶正交级数。证明了关于锥上权函数的正交多项式是二阶微分算子的特征函数，其特征值仅取决于多项式的次数，并且这些多项式的再生核满足一个具有一维特征的封闭公式。后者导致锥上的卷积结构，然后利用它来研究傅立叶正交级数。这一叙述在一定程度上也适用于更一般的权重函数类别。此外，对于锥面上的正交结构，也建立了类似的结果。
Orthogonal polynomials and the Fourier orthogonal series on a cone inare studied. It is shown that orthogonal polynomials with respect to the weight functionon the coneare eigenfunctions of a second order differential operator, with eigenvalues depending only on the degree of the polynomials, and the reproducing kernels of these polynomials satisfy a closed formula that has a one-dimensional characteristic. The latter leads to a convolution structure on the cone, which is then utilized to study the Fourier orthogonal series. This narrative also holds, in part, for more general classes of weight functions. Furthermore, analogous results are also established for orthogonal structure on the surface of the cone.