On the Representation and the Uniform Polynomial Approximation of Polyanalytic Functions of Gevrey Type on the Unit Disk

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 Nanalytic 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 Nanalytic polynomials.