RATIONAL APPROXIMATION IN L φ SPACES ON A FINITE UNION OF DISJOINT INTERVALS - Cuenya, H. H.; Rodriguez, C. N. (Numerical functional analysis and optimization, 2002)
In this paper we study the convergence of the best rational approximants, to a function f, respect to the Luxemburg norm on a finite union of disjoint intervals, with diameters shrinking to zero. This work extends previous results on L p spaces. We also prove existence of best local quasi-rational approximants on a finite point set.