Ideas and Methods in Mathematical Analysis, Stochastics, and Applications: Volume 1 de Sergio Albeverio

Ideas and Methods in Mathematical Analysis, Stochastics, and Applications: Volume 1: In Memory of Raphael Høegh-Krohn

Sergio Albeverio

Helge Holden

Jens Erik Fenstad

Tom Lindstrøm

These volumes contain a collection of essays by many of the closest co-workers of Raphael Høegh-Krohn, 1938–88, one of the outstanding mathematical physicists of our age. The contributions vary in style, purpose, and content - some are surveys where leading experts sum up 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. Many of the papers are based on talks given at a symposium in honor of Høegh-Krohn at the University of Oslo: however the final volumes are far more than proceedings and great care has been taken to attract contributions from the leading researchers.

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Cuprins

Preface; Picture of Raphael Høegh-Krohn; Bibliography of Raphael Høegh-Krohn; 1. On the scientific work of Raphael Høegh-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 Schrödinger 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 représentations 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.