球面上Fourier-Laplace级数线性求和法的饱和问题

SATURATION PROBLEM OF LINEAR METHODS OF FOURIER-LAPLACE SERIES SERIES ON THE SPHERE

详细研究了球面上借助于下三角矩阵Λ确定的Fourier-Laplace级数线性求和法的饱和问题．系统地给出了线性求和法的充分条件及饱和阶；使用Stepanets引入的ψ-导数清楚地刻画出饱和类．

For Fourier-Laplace series on the sphere, the probleme of linear methods generated by lower triangular metrix A are investigated in details. That is, on one hand, the suficient conditions for saturation of linear methods of Fourier- Laplace series and satufation orders are systematicly given, on the other hand, saturation classes are clearly given by using -derivative which Stepannets given first.