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Bochner’s Theorems in the Framework of Quaternion Analysis

  • S. GeorgievEmail author
  • J. Morais
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

Let σ(x) be a nondecreasing function, such that σ(-∞) = 0,σ(-∞) = 1 a nd let us denote by B the class of functions which can be represented by a Fourier–Stieltjes integral \(f(t)=\int^\infty_{-\infty}\;e^{itx}d\sigma(x)\). The purpose of this chapter is to give a characterization of the class B and to give a generalization of the classical theorem of Bochner in the framework of quaternion analysis.

Keywords

Quaternion analysis quaternion Fourier transform quaternion Fourier–Stieltjes integral Bochner theorem 

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References

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of Differential EquationsUniversity of SofiaSofiaBulgaria
  2. 2.Centro de Investigação e Desenvolvimento em Matemática e Aplicações (CIDMA)Universidade de AveiroAveiroPortugal

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