具有多个零点的$A^*$权的一致多项式逼近
Uniform polynomial approximation with $A^*$ weights having finitely many zeros
摘要：
我们证明了匹配的正逆定理均匀多项式逼近与$A^*$权重（一个子类的加倍权重适合近似的$L_\infty$规范）有许多零，而不是太“迅速改变”远离这些零。这类权是相当广泛的，特别是，包括经典的Jacobi权，广义Jacobi权和广义Ditzian-Totik权。引入了主部加权光滑模和完全加权光滑模，研究了它们的性质，并讨论了涉及相关实现泛函的等价型结果。
英文摘要：
We prove matching direct and inverse theorems for uniform polynomial approximation with $A^*$ weights (a subclass of doubling weights suitable for approximation in the $L_\infty$ norm) having finitely many zeros and not too "rapidly changing" away from these zeros. This class of weights is rather wide and, in particular, includes the classical Jacobi weights, generalized Jacobi weights and generalized Ditzian-Totik weights. Main part and complete weighted moduli of smoothness are introduced, their properties are investigated, and equivalence type results involving related realization functionals are discussed.
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