Journal of Applied Mathematics
Volume 2012 (2012), Article ID 175292, 13 pages
http://dx.doi.org/10.1155/2012/175292
Research Article

Calculation of the Reproducing Kernel on the Reproducing Kernel Space with Weighted Integral

Er Gao,1,2 Songhe Song,1,2 and Xinjian Zhang1

1Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha 410073, China
2State key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China

Received 28 April 2012; Accepted 19 July 2012

Academic Editor: Livija Cveticanin

Copyright © 2012 Er Gao et al. 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

We provide a new definition for reproducing kernel space with weighted integral and present a method to construct and calculate the reproducing kernel for the space. The new reproducing kernel space is an enlarged reproducing kernel space, which contains the traditional reproducing kernel space. The proposed method of this paper is a universal method and is suitable for the case of that the weight is variable. Obviously, this new method will generalize a number of applications of reproducing kernel theory to many areas.