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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 28, Pages 1455-1462

On the denseness of Jacobi polynomials

Department of Mathematics/ Computer Applications, Government Model Science College, APS University, Rewa, Madhya 486001, India

Received 29 May 2003

Copyright © 2004 Hindawi Publishing Corporation. 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 X represent either a space C[1,1] or Lα,βp(w), 1p<, of functions on [1,1]. It is well known that X are Banach spaces under the sup and the p-norms, respectively. We prove that there exist the best possible normalized Banach subspaces Xα,βk of X such that the system of Jacobi polynomials is densely spread on these, or, in other words, each fXα,βk can be represented by a linear combination of Jacobi polynomials to any degree of accuracy. Explicit representation for fXα,βk has been given.