Harmonic Analysis and Hypergroups

Under the guidance and inspiration of Dr. Ajit Iqbal Singh, an International Conference on Harmonie Analysis took place at the Uni versity of Delhi, India, from December 18 to 22, 1995. Twenty-one dis tinguished mathematicians from around the world, as weIl as many from India, participated in this successful and stimulating conference. An underlying theme of the conference was hypergroups, the the ory of wh ich has developed and been found useful in fields as diverse as special functions, differential equations, probability theory, representa tion theory, measure theory, Hopf algebras and quantum groups. Some other areas of emphasis that emerged were harmonie analysis of analytic functions, ergo die theory and wavelets. This book includes most of the proceedings of this conference. I chaired the Editorial Board for this publication; the other members were J. M. Anderson (University College London), G. L. Litvinov (Centre for Optimization and Mathematical Modeling, Institute for New Technolo gies, Moscow), Mrs. A. I. Singh (University ofDelhi, India), V. S. Sunder (Institute of Mathematical Sciences, C. LT. , Madras, India), and N. J. Wildberger (University of New South Wales, Australia). I appreciate all the help provided by these editors as weIl as the help and cooperation of Our authors and referees of their papers. I especially appreciate techni cial assistance and advice from Alan L. Schwartz (University of Missouri - St. Louis, USA) and Martin E. Walter (University of Colorado, USA). Finally, I thank Our editor, Ann Kostant, for her help and encouragement during this project.

De Branges Modules in H2(Ck). - Some Methods to Find Moment Functions on Hypergroups. - About Some Random Fourier Series and Multipliers Theorems on Compact Commutative Hypergroups. - Disintegration of Measures. - Multipliers of de Branges-Rovnyak spaces II. - On Hartman Uniform Distribution and Measures on Compact Spaces. - Hypergroups and Signed Hypergroups. - Three lectures on Hypergroups: Delhi, December 1995. - Harmonic Analysis and Functional Equations. - Actions of Finite Hypergroups and Examples. - Positivity of Turán Determinants for Orthogonal Polynomials. - Wavelets on Hypergroups. - Semigroups of Positive Definite Functions and Related Topics. - Characters, Bi-Modules and Representations in Lie Group Harmonic Analysis. - A Limit Theorem on a Family of Infinite Joins of Hypergroups.