Faber polynomial approximation of entire functions of slow growth over Jordan domains

Abstract

In this paper, we study the \(L^p\)-approximation, \(2\le p \le \infty \), of entire functions over Jordan domains by using Faber polynomials. Moreover, the coefficient characterizations of generalized order and generalized type of entire functions for slow growth have been obtained in terms of the \(L^p\)-approximation errors. Our results improve the various results of Seremeta (Am Math Soc Transl Ser 2 88:291–301, 1970) and Ganti and Srivastava (Commun Math Anal 7(1):75–93, 2009).