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Archiv der Mathematik

, Volume 88, Issue 2, pp 153–163 | Cite as

On the growth type of entire monogenic functions

  • D. Constales
  • R. De Almeida
  • R. S. Krausshar
Article

Abstract.

In this paper we establish an explicit relation between the growth type of general entire solutions to the generalized Cauchy-Riemann system in \({\mathbb{R}^{n+1}}\) and their Taylor coefficients. This formula then enables us to compute the growth type of some higher dimensional generalizations of the trigonometric and special functions that are null-solutions to this system.

Mathematics Subject Classification (2000).

30G35 30D15 

Keywords.

Generalized Cauchy-Riemann system entire monogenic functions growth type special functions generalized trigonometric functions 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • D. Constales
    • 1
  • R. De Almeida
    • 2
  • R. S. Krausshar
    • 3
  1. 1.Department of Mathematical AnalysisGhent UniversityGhentBelgium
  2. 2.Departamento de MatemáticaUniversidade de Trás-os-Montes e Alto DouroVila RealPortugal
  3. 3.Department of Mathematics, Section of AnalysisKatholieke Universiteit LeuvenLeuvenBelgium

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