A transform involving Chebyshev polynomials and its inversion formula

  1. Ciaurri, O. 1
  2. Navas, L.M. 2
  3. Varona, J.L. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad de Salamanca
    info

    Universidad de Salamanca

    Salamanca, España

    ROR https://ror.org/02f40zc51

Journal:
Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Year of publication: 2006

Volume: 323

Issue: 1

Pages: 57-62

Type: Article

DOI: 10.1016/J.JMAA.2005.10.028 SCOPUS: 2-s2.0-33747811100 WoS: WOS:000240566000006 GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Journal of Mathematical Analysis and Applications

Abstract

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.