Ideas and Methods in Mathematical Analysis, Stochastics, and Applications: In Memory of Raphael Høegh-Krohn

by Edited by Sergio Albeverio , Helge Holden , Jens Erik Fenstad , Tom Lindstrøm

• ISBN13: 9780521419291
• ISBN10: 0521419298
• Format: Hardcover
• Copyright: 1992-06-26
• Publisher: Cambridge University Press

Summary

These volumes contain a collection of essays by many of the closest co-workers of Raphael Hoegh-Krohn (1938-1988), one of the outstanding mathematical physicists of our age. The contributions vary in style, purpose, and content--some are surveys that summarize and clarify a subject area, others are new and adventurous expeditions into unknown territory. The topics cover most aspects of modern mathematical physics with special emphasis on methods from operator theory and stochastic analysis. Volume 1 contains papers on mathematical analysis (both linear and nonlinear), stochastics, and applications. Volume 2 discusses mathematical problems in quantum and statistical physics.

Table of Contents

Preface

Picture of Raphael Hø

egh-Krohn

Bibliography of Raphael Hø

egh-Krohn

1. On the scientific work of Raphael Hø

egh-Krohn

Part I. Stochastic Analysis

2. Some Euclidean integer-valued random fields with Markov properties

3. A Beurling-Deny type structure theorem for Dirichlet forms on general state spaces

4. Log-concavity of radial Schrö

dinger wave functions and convergence of planetesimal diffusions

5. Dirichlet forms, diffusion processes and spectral dimensions for nested fractals

6. Large deviations for weak solutions of stochastic differential equations

7. On a class of probabilistic integrodifferential equations

8. Operator integrals and martingale integrals with general parameter

9. Wick multiplication and Ito-Skorohod stochastic differential equations

10. Multiscale analysis in random dynamics

11. A limiting distribution connected with fractional parts of linear forms

12. Rapport sur les repré

sentations chaotiques

13. Markov properties of solutions of stochastic partial differential equations in a finite volume

14. On stochastic evolution equations with non-homogeneous boundary conditions

15. Grey noise

16. Existence of invariant measures for diffusion process with infinite dimensional state space

Part II. Infinite Dimensional Groups

17. On nonlinear equations associated with Lie algebras of diffeomorphism groups of two-dimensional manifolds

18. Fields of left-invariant standard Brownian motion processes on a smooth bundle of compact-simple Lie groups

19. Unitary highest weight representations of gauge groups

Part III. Operator Algebras

20. Some non-commutative orbifolds

21. Ergodic actions of non-abelian compact groups

22. Positive projections onto Jordan algebras and their enveloping von Neumann algebras

Part IV. Nonlinear Analysis and Applications

23. How many singularities can there be in an energy minimizing map from the ball to the sphere? 24. Front tracking for petroleum reservoirs

25. Quasi-periodic, finite-gap solutions of the modified Korteweg-de Vries equations

26. A new representation of soliton solutions of the Kadomtsev-Petviashvili equation

27. On scalar conservation laws in one dimension.