A Cohen Type Inequality for Fourier Expansions of Orthogonal Polynomials with a Nondiscrete Jacobi-Sobolev Inner Product

被引：0
作者：
BujarXh Fejzullahu
Francisco Marcellán
机构：
[1] University of Prishtina,Department of Mathematics, Faculty of Mathematics and Natural Sciences
[2] Universidad Carlos III de Madrid,Departamento de Matemáticas, Escuela Politécnica Superior
来源：
Journal of Inequalities and Applications | / 2010卷
关键词：
Orthogonal Polynomial; Fourier Expansion; Jacobi Polynomial; Sobolev Norm; Extremal Property;
D O I：
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摘要：
Let [inline-graphic not available: see fulltext] denote the sequence of polynomials orthogonal with respect to the non-discrete Sobolev inner product [inline-graphic not available: see fulltext], where [inline-graphic not available: see fulltext] and [inline-graphic not available: see fulltext] with [inline-graphic not available: see fulltext], [inline-graphic not available: see fulltext]. In this paper, we prove a Cohen type inequality for the Fourier expansion in terms of the orthogonal polynomials [inline-graphic not available: see fulltext] Necessary conditions for the norm convergence of such a Fourier expansion are given. Finally, the failure of almost everywhere convergence of the Fourier expansion of a function in terms of the orthogonal polynomials associated with the above Sobolev inner product is proved.
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