On the denseness of Jacobi polynomials

Sarjoo Prasad Yadav

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-8

Abstract:

Let X represent either a space C [ − 1 , 1 ] or L α , β p ( w ) , 1 ≤ p < ∞ , 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 X α , β k of X such that the system of Jacobi polynomials is densely spread on these, or, in other words, each f ∈ X α , β k can be represented by a linear combination of Jacobi polynomials to any degree of accuracy. Explicit representation for f ∈ X α , β k has been given.

Date: 2004
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2004/391858.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2004/391858.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:391858

DOI: 10.1155/S0161171204305314

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().