This dissertation is to discuss mainly the common zeros and the reproducing kernels of multivariate orthogonal polynomials, and the orthogonal polynomials on the unit sphere Sd-1. ( 1) We consider the common zeros of multivariate orthogonal polynomials under the Gauss-type case. 本文主要是针对多元正交多项式的公共零点和再生核,以及单位球面Sd-1上正交多项式的一些研究工作。主要工作如下:(1)考虑Gauss-型线性泛函下多元正交多项式的公共零点。