A transform involving Chebyshev polynomials and its inversion formula

被引：3

作者：

Ciaurri, Oscar

Navas, Luis M.

Varona, Juan L.

机构：

[1] Univ La Rioja, Dept Matemat & Computac, Logrono 26004, Spain

[2] Univ Salamanca, Dept Matemat, E-37008 Salamanca, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2006年 / 323卷 / 01期

关键词：

Chebyshev polynomials; Mobius function; Mobius transform; Dirichlet convolution; inversion formula;

D O I：

10.1016/j.jmaa.2005.10.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define a functional analytic transform involving the Chebyshev polynomials T-n (x), with an inversion formula in which the Mobius function mu(n) appears. If s epsilon C with Re(s) > 1, then given a bounded function from [-1, 1] into C, or from C into itself, the following inversion formula holds: [GRAPHICS] if and only if [GRAPHICS] Some other similar results are given. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：57 / 62

页数：6