International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 28, Pages 1455-1462
On the denseness of Jacobi polynomials
Department of Mathematics/ Computer Applications, Government Model Science College, APS University, Rewa 486001, Madhya, India
Received 29 May 2003
Copyright © 2004 Sarjoo Prasad Yadav. 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.
Let represent either a space or , , of functions on . It is well known that are Banach spaces under the sup and the -norms, respectively. We prove that there exist the best possible normalized Banach subspaces of such that the system of Jacobi polynomials is densely spread on these, or, in other words, each can be represented by a linear combination of Jacobi polynomials to any degree of accuracy. Explicit representation for has been given.