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.
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