More approximation on disks
Peter de Paepe,Jan Wiegerinck +1 more
TL;DR: In this paper, the authors studied the function algebra generated by z 2 and g 2 on a small closed disk centred at the origin of the complex plane and proved, using a biholomorphic change of coordinates, that for a large class of functions g this algebra consists of all continuous functions on the disk.
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Abstract: In this article we study the function algebra generated by z 2 and g 2 on a small closed disk centred at the origin of the complex plane. We prove, using a biholomorphic change of coordinates and already developed techniques in this area, that for a large class of functions g this algebra consists of all continuous functions on the disk.
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Citations
Polynomial Convexity and Polynomial Approximations of Certain Sets in C 2 n with Non-isolated CR-Singularities
TL;DR: In this paper , it was shown that under a certain condition on R j , the graph is polynomially convex, and holomorphic polynomorphisms on the graph approximate all continuous functions.
Polynomial Convexity and Polynomial Approximations of Certain Sets in $$\mathbb {C}^{2n}$$ with Non-isolated CR-Singularities
TL;DR: In this article , the authors considered the graph of graphs with non-isolated CR-singularities and showed that the graph is polynomially convex, and holomorphic polynomial functions on the graph approximate all continuous functions.
Uniform approximation on disc
TL;DR: In this article , it was shown that if at least one qj is non-constant, the uniform algebra generated by z and q1(z) is dense in C(D) provided gcd Ω(l,m)=1.
References
Approximation on disks
P. J. de Paepe
- 01 Feb 1986
TL;DR: In this paper, it was 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 zm and zn 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.
Enveloppes polynomiales d'unions de plans réels dans ${\Bbb C}^n$
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