关于多元无界连续函数逼近的渐近估计

On the asymptotic formulae of approximation of multivariate unbounded continuous functions

讨论了多元无界连续函数逼近的渐近估计.利用扩展乘数法讨论了多元线性正算子改造为逼近多元无界连续函数的渐近估计,给出了具有一般性的较为实用的渐近公式.作为实例,研究了多元非乘积型的Landau多项式算子逼近多元无界连续函数的渐近估计式,推广了前人的若干结论.

The asymptotic formulae of approximation of multivariate unbounded continuous functions is studied.By using the method of multiplier-enlargement,the asymptotic estimation of approximation of multivariate unbounded continuous functions with positive linear operators is discussed,and general asymptotic formulae is given.As an example,the asymptotic formulae of approximation of multivariate unbounded continuous functions with Landau operators are discussed,and therefore some conclusions of professor Hsu Lizhi are generalized.