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

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....

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Bibliographic Details
Published in:Communications in mathematical physics Vol. 361; no. 2; pp. 583 - 604
Main Authors: Bożejko, Marek, Gal, Światosław R., Młotkowski, Wojciech
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2018
Springer Nature B.V
Subjects:
Classical and Quantum Gravitation
Color
Complex Systems
Fourier analysis
Harmonic analysis
Mathematical and Computational Physics
Mathematical Physics
Operators (mathematics)
Permutations
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
ISSN:0010-3616, 1432-0916
Online Access:Get full text
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Summary: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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ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-018-3160-6