Geodesic
Degree of Approximation by Rational Functions with Prescribed Numerator Degree
Canadian journal of mathematics, Tome 46 (1994) no. 3, pp. 619-633

Voir la notice de l'article provenant de la source Cambridge University Press

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 Rl,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 ωφ 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.
DOI : 10.4153/CJM-1994-033-1
Mots-clés : 41A20, 41A25, rational approximation, real rational approximation, Jackson theorems, moduli of continuity, prescribed numerator degree 
Leviatan, D.; Lubinsky, D. S. Degree of Approximation by Rational Functions with Prescribed Numerator Degree. Canadian journal of mathematics, Tome 46 (1994) no. 3, pp. 619-633. doi: 10.4153/CJM-1994-033-1
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