Infinite-Dimensional Systems Proceedings of the Conference on Operat
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Infi nite-Dimensional Systems Proceedings of the Conference on Operator Semigroups and Applications held in Retzhof (Styria), Austria, June 5-11, 1983
Edited by F. Kappel and W. Schappacher
Springer-verlag Berlin Heidelberg New York Tokyo 1984
Editors Franz Kappel Wilhelm Schappacher Institut fur Mathematik, Karl-Franzens-Universitat Graz ElisabethstraBe 16,8010 Graz, Austria
AMS Subject Classifications (1980): 34G10, 34G20, 47 H20; 45K05, 49A10, 92A15 ISBN 3-540-13376-3 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-13376-3 Springer-Verlag New York Heidelberg Berlin Tokyo 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 ·Verwertungsgesellschaft Wort', Munich.
© by Springer-Verlag Berlin Heidelberg 1984 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210
PRE F ACE
This volume comprises the proceedings of the "Conference on Operator Semigroups and Applications" held at the Volksbildungsheim SchloB Retzhof (Styria), June
5 - 11, 1983.
The aim of this conference was to stimulate the exchange of ideas and methods and to provide information on recent advances in various directions of research as for instance, integral- and integrodifferential equations, age-dependent population dynamics, approximation methods. It was a great pleasure for us to welcome 42 scientists coming from 12 different countries. Our thanks go to the lecturers, to all participants and especially to the authors of the papers contained in this volume. The conference was made possible by financial support from the Amt der Steiermarkischen Landesregierung and from the Bundesministerium fur Wissenschaft und Forschung. It is a pleasant duty to thank these institutions for their support. In particular we want to thank the staff of the Volksbildungsheim Retzhof, especially Director Dr. Wolfried Filek-Wittinghaus and Dr. Markus Jaroschka for all their efforts which made our stay so pleasant. Special thanks, finally, go to Mrs. G. Krois for her excellent typing of the manuscripts for these proceedings as well as for her help in all administrative affairs. April 1984
F. Kappel W. Schappacher
CON TEN T S
List of Participants W. Arendt GENERATORS OF POSITIVE SEMIGROUPS
M. E. Bal16tti and J. A. Goldstein
VII 1
16
WIENER'S THEOREM AND SEMIGROUPS OF OPERATORS S. N. Busenberg A CLASS OF NONLINEAR DIFFUSION PROBLEMS
23
Ph. Clement ON ABSTRACT VOLTERRA EQUATIONS IN BANACH SPACES WITH COMPLETELY POSITIVE KERNELS
32
K. L. Cooke STABILITY OF NON-AUTONOMOUS DELAY DIFFERENTIAL EQUATIONS BY LIAPUNOV FUNCTIONALS
41
G. Da Prato ABSTRACT DIFFERENTIAL EQUATIONS AND EXTRAPOLATION SPACES
53
G. W. Desch, R. Grimmer and M. Zeman WAVE PROPAGATION FOR ABSTRAC
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