Pointwise Convergence of Fourier Series on the Unit Sphere of R4 with the Quaternionic Setting

  • Shuang Liu
  • Tao Qian
Part of the Trends in Mathematics book series (TM)


We offer a new approach to convergence of Fourier series on the unit sphere of the four-dimensional Euclidean space. The approach is via the quaternionic analysis setting with a crucial application of Fueter’s theorem. Analogs to the Riemann-Lebesgue theorem, localization principle and a Dini’s type pointwise convergence theorem are proved.


Quaternion space Fourier series unit sphere Dini’s type pointwise convergence theorems Fueter’s theorem 

Mathematics Subject Classification (2000)

Primary 42B05,30G35 Secondary 42C10 


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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Shuang Liu
    • 1
  • Tao Qian
    • 1
  1. 1.Faculty of Science and TechnologyUniversity of MacauMacauChina

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