Möbius inversion formulas for flows of arithmetic semigroup

  1. Benito, M. 1
  2. Navas, L.M. 2
  3. Varona, J.L. 3
  1. 1 Instituto Sagasta, Glorieta del Doctor Zubía s/n, 26003 Logroño, Spain
  2. 2 Universidad de Salamanca

    Universidad de Salamanca

    Salamanca, España

    ROR https://ror.org/02f40zc51

  3. 3 Universidad de La Rioja

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal of Number Theory

ISSN: 0022-314X

Year of publication: 2008

Volume: 128

Issue: 2

Pages: 390-412

Type: Article

DOI: 10.1016/J.JNT.2007.04.009 SCOPUS: 2-s2.0-36749036605 WoS: WOS:000207498600009 GOOGLE SCHOLAR lock_openOpen access editor

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We define a convolution-like operator which transforms functions on a space X via functions on an arithmetical semigroup S, when there is an action or flow of S on X. This operator includes the well-known classical Möbius transforms and associated inversion formulas as special cases. It is defined in a sufficiently general context so as to emphasize the universal and functorial aspects of arithmetical Möbius inversion. We give general analytic conditions guaranteeing the existence of the transform and the validity of the corresponding inversion formulas, in terms of operators on certain function spaces. A number of examples are studied that illustrate the advantages of the convolutional point of view for obtaining new inversion formulas. © 2007 Elsevier Inc. All rights reserved.