Approximation on disks. (English) Zbl 0593.46045
It is shown that if the functions F and G are defined in a neighborhood of the origin in the complex plane and are in a certain sense like \(z^ m\) and \(\bar z^ n\) with \(\gcd (m,n)=1\), then on sufficiently small closed disks D around 0 every continuous function on D can be uniformly approximated by polynomials in F and G.
MSC:
46J10 | Banach algebras of continuous functions, function algebras |
41A10 | Approximation by polynomials |