Best Polynomial Approximation in -Norm and -Growth of Entire Functions

Best Polynomial Approximation in L-Norm and (p, q)-Growth of Entire Functions

and Applied Analysis 3 which vanishes on K except perhaps for a pluripolar subset and satisfies the complex Monge-Ampère equation (see [12]): (dd c V K ) n = 0 on Cn \ K. (16) If n = 1, the Monge-Ampère equation reduces to the classical Laplace equation. For this reason, the functionV K is considered as a natural counterpart of the classical Green function with logarithmic pole at infinity and ...

Coupled systems of equations with entire and polynomial functions

We consider the coupled system$F(x,y)=G(x,y)=0$,where$$F(x, y)=bs 0 {m_1}   A_k(y)x^{m_1-k}mbox{ and } G(x, y)=bs 0 {m_2} B_k(y)x^{m_2-k}$$with entire functions $A_k(y), B_k(y)$.We    derive a priory estimates  for the sums of the rootsof the considered system andfor the counting function of  roots.

The best uniform polynomial approximation of two classes of rational functions

In this paper we obtain the explicit form of the best uniform polynomial approximations out of Pn of two classes of rational functions using properties of Chebyshev polynomials. In this way we present some new theorems and lemmas. Some examples will be given to support the results.

The best approximation of some rational functions in uniform norm

Here we are concerned with the best approximation by polynomials to rational functions in the uniform norm. We give some new theorems about the best approximation of 1/(1 + x) and 1/(x − a) where a > 1. Finally we extend this problem to that of computing the best approximation of the Chebyshev expansion in uniform norm and give some results and conjectures about this.  2005 IMACS. Published by...

Generalized Order and Best Approximation of Entire Function in Lp-Norm