A transform involving Chebyshev polynomials and its inversion formula
We define a functional analytic transform involving the Chebyshev polynomials Tn (x), with an inversion formula in which the Möbius function μ (n) appears. If s ∈ 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:g...
| Autores: | , , |
|---|---|
| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2006 |
| País: | España |
| Recursos: | Universidad de La Rioja (UR) |
| Repositorio: | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| OAI Identifier: | oai:portal.dialnet.es:doc/5bbc69c8b750603269e8215b |
| Acesso em linha: | https://investigacion.unirioja.es/documentos/5bbc69c8b750603269e8215b |
| Access Level: | acceso abierto |
| Palavra-chave: | Chebyshev polynomials Dirichlet convolution Inversion formula Möbius function Möbius transform |
| Resumo: | We define a functional analytic transform involving the Chebyshev polynomials Tn (x), with an inversion formula in which the Möbius function μ (n) appears. If s ∈ 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:g (x) = underover(∑, n = 1, ∞) frac(1, ns) f (Tn (x)) if and only iff (x) = underover(∑, n = 1, ∞) frac(μ (n), ns) g (Tn (x)) . Some other similar results are given. © 2005 Elsevier Inc. All rights reserved. |
|---|