关于多元多项式逼近的一些结果

SOME RESULTS ON MULTIVARIATE POLYNOMIAL APPROXIMATIONS

本文首先用积分型线性正算子实现了C（［-π,π］m×［-α,α］k）上多元代数与三角多项式的混合逼近．进而，通过构造更具体的乘积核，还得到了C（［-π,π］m）上三角逼近的。维Rogosinski型逼近定理及Cr（［-1，1］k）上k维代数多项式逼近的Timan型定理．

This paper realizes first the multivariate algebraic and triangular polynomial approximations on C([-π, π］m × [-a, a]k) with some general integral-type positive linearoperator. Then constructing certain specific product kernels, we have obtained the Rogosinskitype theorem of m-dimensional triangular approximation on C([-π, π］m, and the Timan-typetheorem of k-dimensional algebraic polynomial approximation on Cr([-1, 1]k).