English

On the representation and the uniform polynomial approximation of polyanalytic functions of Gevrey type on the unit disk

Complex Variables 2020-02-11 v1

Abstract

In this paper we define Gevrey polyanalytic classes of order N on the unit disk D and we obtain for these classes a characteristic expansion into N-analytic polynomials on suitable neighborhoods of D. As an application of our main theorem, we perform for the Gevrey polyanalytic classes of order N on the unit disk D, an analogue to E. M. Dyn'kin's theorem. We also derive, for these classes, their characteristic degree of the best uniform approximation on D by N-analytic polynomials.

Keywords

Cite

@article{arxiv.2002.03777,
  title  = {On the representation and the uniform polynomial approximation of polyanalytic functions of Gevrey type on the unit disk},
  author = {Hicham Zoubeir and Samir Kabbaj},
  journal= {arXiv preprint arXiv:2002.03777},
  year   = {2020}
}

Comments

23 pages