Journal of Applied Mathematics 
Volume 2 (2002), Issue 2, Pages 51-69
doi:10.1155/S1110757X02112125

Integral representations for Padé-type operators

Nicholas J. Daras1,2

 1Department of Mathematics, Hellenic Air Force Academy, Dekeleia Attikis, Greece
2Jean Moreas 19, 152 32 Chalandri, Athens, Greece
Received 2 October 2000; Revised 10 October 2001

Abstract

The main purpose of this paper is to consider an explicit form of the Padé-type operators. To do so, we consider the representation of Padé-type approximants to the Fourier series of the harmonic functions in the open disk and of the L p-functions on the circle by means of integral formulas, and, then we define the corresponding Padé-type operators. We are also oncerned with the properties of these integral operators and, in this connection, we prove some convergence results.