Journal of Applied Mathematics
Volume 2 (2002), Issue 2, Pages 51-69
doi:10.1155/S1110757X02112125
Integral representations for Padé-type operators
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
Copyright © 2002 Nicholas J. Daras. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.