Symposium on Probability Methods in Analysis
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Symposium on Probability Methods in Analysis Lectures delivered at a symposium at Loutraki, Greece, 22. 5. - 4. 6. 1966 Chairman: Professor D. A. Kappos
1967
Springer-Verlag · Berlin Heidelberg· New York
This symposium was supported by the ScientifIC Affairs Divisions of the North Atlantic Treaty Organization.
All rights, especially that of translation into foreign languages, reserved. It is also forbidden to reproduce this book, either whole or in part, by photomecha.nJcal means (photostat, microfllm and/or microcard) or by other procedure without writl:eb pennission from Springer Verlag. C by Springer-Verlag Berlin' Heidelberg 1967. Library of Co__ren Catalog Card Number 67-16670. Printed in Ge1'lD&D.y. Title No. 7351.
Contents Remarques sur les Theoremes de Bochner et P. Levy (A. Badrikian)
1
Recent developments in Axiomatic Potential Theory (R. Bauer)
20
Uber wesentlich indefinite Spiele (D. Bierlein)
28
La Topologie fine en Theorie du Potential (M. Brelot)
36
Lois Stables et Espaces (J. Bretagnolle, D. DacunhaCastelle, et J. L. Krivine) 48 Comments on the Martingale Convergence Theorem (S. D. Chatterji)
55
Faktorisierung von Differentialoperationen (R. Dinges)
62
Die Anzahl der Niveaudurchgange und der lokalen Maximal stellen von GauBschen Prozessen (W. Fieger) 63 Vektorwertige Masse und Zufallsvariable auf Boolesche Algebren und der Satz von RadonNikodym (P. Georgiou)
69
Toward a Theory of Patterns (U. Grenander)
79
On the Potential Theory of Linear, Homogeneous Parabolic Partial Differential Equations of Second Order (S.Guber) 112 Invariant and noninvariant Measures (K. Jacobs)
118
Representation of Abstract LSpaces (D. A. Kappos)
136
Extensions of stationary Processes (R. G. Kellerer)
146
Renewal Sequences and their Arithmetic (D. G. Kendall) 147 Optimal Bounded Control with Linear Stochastic Equations and Quadratic Cost (E. Kounias) 176
On a Fourier Transform in Infinitely many Dimensions (P. Kristensen, L. Mejlbo, and E.T. Poulsen)
187
Some Problems Arising from Spectral Analysis (R. M. Loynes)
197
Analytical Methods in Probability Theory (E. Lukacs)
208
a
Martingales Valeurs Vectorielles Application Derivation (M. Metivier)
a la
239
Atomes Conditionnels d'Espaces de Probalite de l'Information (J. Neveu) 256 On Markov Processes whose Shift Transformation is quasimixing (F. Papangelou) 272 Remarks on the Poisson Process (A. Renyi)
280
Sums of Markov-chains on Finite Semigroups (L. Schmetterer) 287 On Superefficiency (L. Schmetterer)
291
The Explicit Martin Boundary Constructions (F. Spitzer) 296 Structure des Lois Indefiniment Divisibles E. 'J.. 'J (t)) dans un Espace Vectoriel Topologique (separe) X (A. Tortrat)
299
On a Paper of J. G. Sinai on Dynamical Systems (H. Zieschang)
329
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Remargues sur les Theoremes de Bochner et P.Leyz par A.Badrikian
Dans Ie calcul des
"classique" un grand rale est
fonction
par la notion
de
Et dans cette direction, les theoremes de Bochner et
sont constamment Nous nous proposons ici de
ces resultats pour
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