Article ID Journal Published Year Pages File Type
4614614 Journal of Mathematical Analysis and Applications 2016 24 Pages PDF
Abstract

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∞L∞ 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.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
Authors
,