A COHEN TYPE INEQUALITY FOR GEGENBAUER-SOBOLEV EXPANSIONS

被引：3

作者：

Fejzullahu, Bujar Xh. ^{[1
]}

Marcellan, Francisco ^{[1
]}

机构：

[1] Univ Carlos III Madrid, Escuela Politecn Super, Dept Matemat, Leganes 28911, Spain

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2013年 / 43卷 / 01期

关键词：

Gegenbauer-Sobolev polynomials; Orthogonal expansions; Cohen type inequality; POLYNOMIALS; RESPECT;

D O I：

10.1216/RMJ-2013-43-1-135

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the Sobolev-type inner product < f, g > = integral(1)(-1) f(x) g(x) d mu(x) + M[f(1) g(1) + f(-1) g(-1)] + N[f' (1)g' (1) + f' (-1)g' (-1)], where d mu(x) = Gamma(2 alpha + 2)/2(2 alpha) + (1)Gamma(2) (alpha + 1) (1 - x(2))(alpha) dx, M, N >= 0, alpha > - 1. 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.

引用

页码：135 / 148

页数：14

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