Type: Article
Publication Date: 1994-06-01
Citations: 8
DOI: https://doi.org/10.4153/cjm-1994-033-1
Abstract We prove a Jackson type theorem for rational functions with prescribed numerator degree: For continuous functions f : [—1,1] —> ℝ with ℓ sign changes in (—1,1), there exists a real rational function R ℓ,n ( x ) with numerator degree ℓ and denominator degree at most n , that changes sign exactly where f does, and such that Here C is independent of f, n and ℓ, and ω φ is the Ditzian-Totik modulus of continuity. For special functions such as f ( x ) = sign( x )| x | α we consider improvements of the Jackson rate.