Probability Measures on Groups X

ISBN-13: 9780306440595 / Angielski / Twarda / 1992 / 498 str.

H. Heyer

Opis

The present volume contains the transactions of the lOth Oberwolfach Conference on "Probability Measures on Groups." The series of these meetings inaugurated in 1970 by L. Schmetterer and the editor is devoted to an intensive exchange of ideas on a subject which developed from the relations between various topics of mathematics: measure theory, probability theory, group theory, harmonic analysis, special functions, partial differential operators, quantum stochastics, just to name the most significant ones. Over the years the fruitful interplay broadened in various directions: new group-related structures such as convolution algebras, generalized translation spaces, hypercomplex systems, and hypergroups arose from generalizations as well as from applications, and a gradual refinement of the combinatorial, Banach-algebraic and Fourier analytic methods led to more precise insights into the theory. In a period of highest specialization in scientific thought the separated minds should be reunited by actively emphasizing similarities, analogies and coincidences between ideas in their fields of research. Although there is no real separation between one field and another - David Hilbert denied even the existence of any difference between pure and applied mathematics - bridges between probability theory on one side and algebra, topology and geometry on the other side remain absolutely necessary. They provide a favorable ground for the communication between apparently disjoint research groups and motivate the framework of what is nowadays called "Structural probability theory."

Spis treści

Homoclinic Points CrCreated under Hypotheses by Probability Measures (N. Aoki et al.). An Approximate Martingale Convergence Theorem on Locally Compact Abelian Groups (M.S. Bingham). Positive Definite Functions and the Lévy Continuity Theorem for Commutative Hypergroups (W.R. Bloom et al.). A HuntStein Theorem for Amenable Semigroups (J.S. Bondar). Jacobi Polynomials and Related Hypergroup Structures (W.C. Connett et al.). Discrete Time Voter Models: A Class of Stochastic Autonoma (R.W.R. Darling et al.). Theoretical and Disctributional Aspects of Shape Analysis (I.L. Dryden et al.). Speed of COnvergence of Transformed Convolution Powers of a Probability Measure on a Compact Connected Group (P. Eisele). Krawtchouk Polynomials and Finite Probability Theory (P. Feinsilver et al.). Sur Quelques Transformations Intégrales Multidimensionelles et Leur Lien avec la Théorie des Hypergroupes (L. Gallardo). Critère de Transcience d'un Semi Groupe de Probabilités sur une Classe d'Hypergroupes Commutatifs (M.O. Gebuhrer). Applications of Symmetry Groups in Markov Processes (J. Glover). Classes of Trimeasures: Applications of Harmonic Analysis (C.C. Graham et al.). A Study of Some Stationary Gaussian Processes Indexed by the Homogeneous Tree (C. Hassenforder). 21 additional articles. Index.