Volume 16, Issue 2 (10-2021)                   IJMSI 2021, 16(2): 89-115 | Back to browse issues page


XML Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Kabbaj S, Zoubeir H. On the Representation and the Uniform Polynomial Approximation of Polyanalytic Functions of Gevrey Type on the Unit Disk. IJMSI. 2021; 16 (2) :89-115
URL: http://ijmsi.ir/article-1-1288-en.html
Abstract:  
 In this paper we deÖne Gevrey polyanalytic classes of order N on the unit disk D and we characterize these classes by a speciÖc 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. Dyníkinís theorem. We derive also, for these classes, their characteristic degree of the best uniform approximation on D by Nanalytic polynomials. Keywords: Polyanalytic functions, Gevrey classes, Degree of polynomial approximation. 2000 Mathematics subject classiÖcation: 30D60, 26E05, 41A10. 1. Introduction The polyanalytic functions of order 2, the so-called bianalytic functions, originates from mechanics where they played a fundamental role in solving the problems of the planar theory of elasticity. Their usefulness in mechanics was illustrated by the pioneering works of Kolosso§, Muskhelishvili and their followers (([15])-([17]), [24], [25], [27]). By the systematic use of complex variable techniques these authors have greatly simpliÖed and extended the mathematicalmethods of the elasticity theory. The class of polyanalytic functions of order Corresponding Author 1analytic 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. Dyníkinís theorem. We derive also, for these classes, their characteristic degree of the best uniform approximation on D by Nanalytic polynomials. Keywords: Polyanalytic functions, Gevrey classes, Degree of polynomial approximation. 2000 Mathematics subject classiÖcation: 30D60, 26E05, 41A10. 1. Introduction The polyanalytic functions of order 2, the so-called bianalytic functions, originates from mechanics where they played a fundamental role in solving the problems of the planar theory of elasticity. Their usefulness in mechanics was illustrated by the pioneering works of Kolosso§, Muskhelishvili and their followers (([15])-([17]), [24], [25], [27]). By the systematic use of complex variable techniques these authors have greatly simpliÖed and extended the mathematicalmethods of the elasticity theory. The class of polyanalytic functions of order Corresponding Author 1analytic
polynomials.
Type of Study: Research paper | Subject: General

Add your comments about this article : Your username or Email:
CAPTCHA

Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

© 2021 CC BY-NC 4.0 | Iranian Journal of Mathematical Sciences and Informatics

Designed & Developed by : Yektaweb