Approximation of meromorphic functions by rational functions

Approximation by Rational Functions

Approximation by Rational Functions

Making use of the Hardy-Littlewood maximal function, we give a new proof of the following theorem of Pekarski: If f' is in L log L on a finite interval, then f can be approximated in the uniform norm by rational functions of degree n to an error 0(1/n) on that interval. It is well known that approximation by rational functions of degree n can produce a dramatically smaller error than that for p...

APPROXIMATION OF 3D-PARAMETRIC FUNCTIONS BY BICUBIC B-SPLINE FUNCTIONS

In this paper we propose a method to approximate a parametric 3 D-function by bicubic B-spline functions

Approximation by Rational Functions in

The denseness of rational functions with prescribed poles in the Hardy space and disk algebra is considered. Notations. C complex plane D unit disk fz : jzj < 1g Tunit circle fz : jzj = 1g H p Hardy space of analytic functions on D kfk 1 := supfjf(z)j : z 2 D g, the H 1 norm A(D) disk algebra of functions analytic on D and continuous on D P n set of polynomials of degree at most n

RATIONAL DECOMPOSITIONS OF p-ADIC MEROMORPHIC FUNCTIONS

Let K be a non archimedean algebraically closed field of characteristic π, complete for its ultrametric absolute value. In a recent paper by Escassut and Yang ([6]) polynomial decompositions P (f) = Q(g) for meromorphic functions f , g on K (resp. in a disk d(0, r−) ⊂ K) have been considered, and for a class of polynomials P , Q, estimates for the Nevanlinna function T (ρ, f) have been derived....