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

Hicham Zoubeir; Samir Kabbaj

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arXiv · 2002.03777

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

Hicham Zoubeir·Samir Kabbaj

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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.

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Hicham Zoubeir, Samir Kabbaj. 2020-01-31. On the representation and the uniform polynomial approximation of polyanalytic functions of Gevrey type on the unit disk. https://arxiv.org/abs/2002.03777

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