Acta Mathematica Hungarica

, Volume 151, Issue 2, pp 361–378

A Salem generalised function

  • E. de Amo
  • M. Díaz Carrillo
  • J. Fernández-Sánchez
Article

DOI: 10.1007/s10474-017-0690-x

Cite this article as:
de Amo, E., Carrillo, M.D. & Fernández-Sánchez, J. Acta Math. Hungar. (2017) 151: 361. doi:10.1007/s10474-017-0690-x
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Abstract

Among the members of the celebrated family of functions introduced by Salem in the mid 20th century, there is a particular and very interesting one that we use to relate the dyadic system of numbers representation with the modified Engel system. Various properties are studied for this function, including derivatives and fractal dimensions.

Key words and phrases

singular function Engel representation asymptotic distribution function Hausdorff (fractal) dimension 

Mathematics Subject Classification

26A30 26A24 

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  • E. de Amo
    • 1
  • M. Díaz Carrillo
    • 2
  • J. Fernández-Sánchez
    • 1
  1. 1.Universidad de AlmeríaAlmeríaSpain
  2. 2.Universidad de GranadaGranadaSpain