# Applications of Hypergroups and Related Measure Algebras

Share this page *Edited by *
*William C. Connett; Marc-Olivier Gebuhrer; Alan L. Schwartz*

“The most important single thing about this
conference was that it brought together for the first time
representatives of all major groups of users of hypergroups. [They]
talked to each other about how they were using hypergroups in fields as
diverse as special functions, probability theory, representation theory,
measure algebras, Hopf algebras, and Hecke algebras. This led
to fireworks.”—from the Introduction

Hypergroups occur in a wide variety of contexts, and
mathematicians the world over have been discovering this same
mathematical structure hidden in very different applications. The
diverse viewpoints on the subject have led to the need for a common
perspective, if not a common theory. Presenting the proceedings of a
Joint Summer Research Conference held in Seattle in the summer of 1993,
this book will serve as a valuable starting point and reference tool for
the wide range of users of hypergroups and make it easier for an even
larger audience to use these structures in their work.

# Table of Contents

## Applications of Hypergroups and Related Measure Algebras

- Contents ix10 free
- Preface xi12 free
- Limit theorems for some hypergroup structures on Rn x [0, ∞[ 116 free
- Nuclear spaces of test functions connected with hypercomplex systems and representations of such systems 1530
- Hypercomplex systems and hypergroups: Connections and distinctions 2136
- The Hardy-Littlewood maximal function for Chébli-Trimèche hypergroups 4560
- Sturm-Liouville hypergroups 7186
- Continuous 2-variable polynomial hypergroups 89104
- A survey of Fourier algebras 111126
- Expansion in series of Laguerre functions for solution of perturbed Laguerre equations 129144
- Asymptotic behaviour of the paths of random walks on some commutative hypergroups 135150
- Bounded measures algebras: A fixed point approach 171186
- Progress in the theory of probability on hypergroups 191206
- Discrete hypergroups associated with compact quantum Gelfand pairs 213228
- Transmutation operators and the inverse spectral problem 237252
- Limit theorems for the spin process 245260
- Differential operators with matrix coefficients and transmutations 261276
- Generalized product formula for orthogonal polynomials 269284
- An infinitesimal algebra of the hypergroup generated by double cosets and nonlinear differential equations 287302
- Convolution algebras which are not necessarily positivity-preserving 299314
- Signed hypergroups—a survey 319334
- On the relation between subfactors and hypergroups 331346
- Connection coefficients of orthogonal polynomials with applications to classical orthogonal polynomials 341356
- Generalized transmutation and translation operators associated with partial differential operators 347362
- Gel'fand pairs of quantum groups, hypergroups and q-special functions 373388
- Central limit theorems for Jacobi hypergroups 395410
- Finite commutative hyper groups and applications from group theory to conformal field theory 413428
- Kolmogorov's three series theorem on one-dimensional hypergroups 435450