Uniform polynomial approximation with A^⁎ weights having finitely many zeros

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• 作者：Kirill A. Kopotun¹ ; ^{kopotunk@cc.umanitoba.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Doubling weights ; A⁎A⁎ weights ; Weighted moduli of smoothness ; Polynomial approximation ; Direct and inverse theorems ; Realization functionals
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：435
• 期：1
• 页码：677-700
• 全文大小：479 K

文摘

We prove matching direct and inverse theorems for uniform polynomial approximation with A^⁎$A^{⁎}$ weights (a subclass of doubling weights suitable for approximation in the L_∞${\mathbb{L}}_{\infty }$ 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.