二元Gauss-Weierstrass算子线性组合的一致逼近

Uniform Approximation of Linear Combinations of Binary Gauss-Weierstrass Operators

通过介绍二元Gauss-Weierstrass算子线性组合,并借助K-泛函、光滑模二者之间的关系,首先对二元Gauss-Weierstrass算子的基本性质进行了分析,其次证明了该算子的有界性,最后构建了二元Gauss-Weierstrass算子线性组合在一致逼近意义下的一致逼近性质,并给出了逼近误差的估计。

By introducing the linear combination of binary Gauss-Weierstrass operators,and leveraging the relationship between the K-functions and the smooth moduli,the basic properties of the binary Gauss-Weierstrass operator were analyzed,followed by a proof of its boundedness,and a consistent approximation property in the sense of uniform convergence was constructed for the binary Gauss-Weierstrass operator linear combination in the end.And an estimate of the approximation error was given.