Lecture Notes in Mathematics

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2 Lecture Notes in Mathematics Edited by A Dold and B. Eckmann Series: Universite de Strasbourg Advisor: P.-A Meyer 404 Theone du Potentiel et Analyse Harmonique Edite par Jacques Faraut Universite de Strasbourg, Strasbourg/France Springer-Verlag Berlin Heidelberg NewYork 1974

3 Library of Congress Cataloging in Publication Data du potentiel. du potentiel. (Lecture notes in mathematics, 404) French or English. Bibliography: p. 1. Potential, Theory of--congresses. 2. Harmonic analysis--congresses. I. Faraut, Jacques, ed, II. Series: Lecture notes in mathematics (Berlin) 404. QA3.I28 no. 404 [QA331] 510'.8s [515'.7] AMS Subject Classifications (1970): 43A05,43A25,43A75,34B25, 60B15, 31 C05, 31 C15, 31 C25, 53C35, 60G45, 60J45, 60J60 ISBN Springer-Verlag Berlin' Heidelberg New York ISBN Springer-Verlag New York' Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. by Springer-Verlag Berlin' Heidelberg Printed in Germany. Offsetdruck: Julius Beltz, Hemsbach/Bergstr.

4 INTROVUCTION Ce volume rassemble les exposes des journees de la Societe Mathematique de France qui se sont tenues l'institut de Recherche Mathematique Avancee de Strasbourg les 9, 10 et 11 mai Elles ont ete consacrees aux questions de theorie du potentiel ou intervient l'analyse harmonique comme : noyaux de convolution, semi-groupes de convolution, semi-groupes d'operateurs, representation integrale des fonctions harmoniques positives. Nous joignons ce volume un article de M.M. HIRSCH et ROTH qui traite d'un sujet souvent aborde des conversations de ces journees.

5 CONFERENCES (Copenhague) Sur les semi-groupes de convolution. BLIEDTNER J. (Erlangen) Extreme harmonic functions on groups. 27 CHEBLI H. (Strasbourg) Operateurs de translation generalisee et semi-groupes de convolution. 35 CHOQUET G. (Paris) et (Orsay) Noyaux de convolution et balayage sur tout ouvert. 60 FORST G. (Copenhague) A characterization of non-symmetric translation invariant Dirichlet forms. 113 GUIVARC'H Y. et CONZE J.P. (Rennes) Propriete de droite fixe et fonctions harmoniques positives. 126 HARZALLAH K. (Tunis) Distance hilbertiennes invariantes sur un espace homogene. 133 (Montreal) Generalisations de la notion des classes H p de Hardy. 138 HIRSCH F. (Cachan - Orsay) Transformation de Stieltjes et fonctions operant sur les potentiels abstraits. 149 MALLIAVIN M.P. et MALLIAVIN P. (Paris) Factorisation et lois limites de la diffusion horizontale au-dessus d'un espace riemannien symetrique. 164 TAKAHASHI R. (Nancy) Fonctions spheriques dans les groupes Sp(n,1) 218 HIRSCH F. et ROTH J.P. Operateurs disspatifs et codissipatifs invariants sur un espace homogene. 229