- Research Article
- Open Access
A Cohen-Type Inequality for Jacobi-Sobolev Expansions
- Bujar Xh Fejzullahu1Email author
https://doi.org/10.1155/2007/93815
© Bujar Xh. Fejzullahu 2007
- Received: 21 August 2007
- Accepted: 11 December 2007
- Published: 6 February 2008
Abstract
Let
be the Jacobi measure supported on the interval [-1, 1]. Let us introduce the Sobolev-type inner product
, where
. In this paper we prove a Cohen-type inequality for the Fourier expansion in terms of the orthonormal polynomials associated with the above Sobolev inner product. We follow Dreseler and Soardi (1982) and Markett (1983) papers, where such inequalities were proved for classical orthogonal expansions.
Keywords
- Fourier Expansion
- Orthogonal Expansion
- Orthonormal Polynomial
- Jacobi Measure
Authors’ Affiliations
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Copyright
This article is published under license to BioMed Central Ltd. 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.
