Communications in Mathematical Physics

, Volume 361, Issue 2, pp 583–604 | Cite as

Positive Definite Functions on Coxeter Groups with Applications to Operator Spaces and Noncommutative Probability

  • Marek Bożejko
  • Światosław R. Gal
  • Wojciech MłotkowskiEmail author


A new class of positive definite functions related to colour-length function on arbitrary Coxeter group is introduced. Extensions of positive definite functions, called the Riesz–Coxeter product, from the Riesz product on the Rademacher (Abelian Coxeter) group to arbitrary Coxeter group is obtained. Applications to harmonic analysis, operator spaces and noncommutative probability are presented. Characterization of radial and colour-radial functions on dihedral groups and infinite permutation group are shown.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Marek Bożejko
    • 1
  • Światosław R. Gal
    • 2
  • Wojciech Młotkowski
    • 2
    Email author
  1. 1.Polska Akademia NaukWrocławPoland
  2. 2.Uniwersytet WrocławskiWrocławPoland

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