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1 results

  • Generalized hypergroups and orthogonal polynomials

  • Part of
  • Rupert Lasser, Josef Obermaier, Holger Rauhut
  • Journal:
    Journal of the Australian Mathematical Society / Volume 82 / Issue 3 / June 2007
    Published online by Cambridge University Press:
    09 April 2009, pp. 369-394
    Print publication:
    June 2007
    • Article
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  • The concept of semi-bounded generalized hypergroups (SBG hypergroups) is developed. These hypergroups are more special than generalized hypergroups introduced by Obata and Wildberger and more general than discrete hypergroups or even discrete signed hypergroups. The convolution of measures and functions is studied. In the case of commutativity we define the dual objects and prove some basic theorems of Fourier analysis. Furthermore, we investigate the relationship between orthogonal polynomials and generalized hypergroups. We discuss the Jacobi polynomials as an example.