Contemporary Mathematics 1995; 441 pp; softcover Volume: 183 ISBN10: 0821802976 ISBN13: 9780821802977 List Price: US$89 Member Price: US$71.20 Order Code: CONM/183
 "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. Readership Advanced graduate students and researchers in measure algebras, statisticians and physicists. Table of Contents  N. B. Salem and M. N. Lazhari  Limit theorems for some hypergroup structures on \({\mathbb R}^n\times [0,\infty [\)
 Yu. M. Berezansky  Nuclear spaces of test functions connected with hypercomplex systems and representations of such systems
 Yu. M. Berezansky and A. A. Kalyuzhnyi  Hypercomplex systems and hypergroups: Connections and distinctions
 W. R. Bloom and Z. Xu  The HardyLittlewood maximal function for ChébliTrimèche hypergroups
 H. Chebli  SturmLiouville hypergroups
 W. C. Connett and A. L. Schwartz  Continuous \(2\)variable polynomial hypergroups
 P. Eymard  A survey of Fourier algebras
 A. Fitouhi and M. M. Hamza  Expansion in series of Laguerre functions for solution of perturbed Laguerre equations
 L. Gallardo  Asymptotic behaviour of the paths of random walks on some commutative hypergroups
 M.O. Gebuhrer  Bounded measures algebras: A fixed point approach
 H. Heyer  Progress in the theory of probability on hypergroups
 T. H. Koornwinder  Discrete hypergroups associated with compact quantum Gelfand pairs
 B. M. Levitan  Transmutation operators and the inverse spectral problem
 M. Mabrouki  Limit theorems for the spin process
 N. H. Mahmoud  Differential operators with matrix coefficients and transmutations
 B. P. Osilenker  Generalized product formulas for orthogonal polynomials
 G. B. Podkolzin  An infinitesimal algebra of the hypergroup generated by double cosets and nonlinear differential equations
 M. Rösler  Convolution algebras which are not necessarily positivitypreserving
 K. A. Ross  Signed hypergroupsA survey
 V. S. Sunder  On the relation between subfactors and hypergroups
 R. Szwarc  Connection coefficients of orthogonal polynomials with applications to classical orthogonal polynomials
 K. Trimeche  Generalized transmutation and translation operators associated with partial differential operators
 L. Vainerman  Gel'fand pairs of quantum groups, hypergroups and \(q\)special functions
 M. Voit  Central limit theorems for Jacobi hypergroups
 N. J. Wildberger  Finite commutative hypergroups and applications from group theory to conformal field theory
 H. Zeuner  Kolmogorov's three series theorem on onedimensional hypergroups
