Probability Measures on Groups IX Proceedings of a Conference held i
The latest in this series of Oberwolfach conferences focussed on the interplay between structural probability theory and various other areas of pure and applied mathematics such as Tauberian theory, infinite-dimensional rotation groups, central limit theo
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Edited by A. Oold and B. Eckmann
1379 H. Heyer (Ed.)
Measures on Groups IX Proceedings of a Conference held in Oberwolfach, FRG, January 17-23, 1988
Springer-Verlag Berlin Heidelberg New York London ParisTokyo Hong Kong
Editor
Herbert Heyer Mathematisches Institut, Universitat Tubinqen Auf der Morgenstelle 10, 7400 Tubinqen, Federal Republic of Germany
Mathematics Subject Classification (1980): Primary: 60B15, 60J 15, 60J30, 60G60, 43A05, 43A33, 43A85 Secondary: 31 C25, 33A45, 33A 75, 46L50, 62H 10 ISBN 3-540-51401-5 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-51401-5 Springer-Verlag New York Berlin Heidelberg
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PRE F ACE
The 1988 Conference "Probability Measures on Groups" was designed, in deviation from the previous meetings on the subject, as a forum on which the interplay between structural probability theory and seemingly quite distant topics of pure and applied mathematics were to be discussed and documented. T'he various interrelations were made explicit in the expository talks presented on special
The organizers
are very grateful to their colleagues for having prepared these special talks and for having submitted the underlying manuscripts in elaborated form to the Proceedings. Here is the list of the survey speakers and the titles of their talks N.H. BINGHAM, The Royal Holloway and Bedford New College, Egham, England Tauberian methods in probability theory T.
HIDA, Nagoya University, Nagoya, Japan Infinite dimensional rotation group and unitary group
M.M. RAO, University of California at Riverside, Riverside, USA
Bimeasures and harmonizable processes A. TERRAS, University of California at San Diego, La Jolla, USA The central limit theorem for symmetric spaces of GL(3) G.S. WATSON, Princeton University, Princeton, USA Statistics of rotations. In the following we shall briefly comment on the research contributions contained in this volume. There has been a wide range of topics with some emphasis on convolution semigroups of measures, their potential theory and harmonic analysis. While at the preceding conferences on probability measures on groups the basic structure was mainly a group or a semigroup, the recent development emphasizes more general
structures.
IV
These generalized translation or hypergroup structures, probabilistic in nature, appear in duals o
