Selected Papers of E.B. Dynkin with Commentary

Front Cover
American Mathematical Soc., 2000 - Mathematics - 798 pages
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Eugene Dynkin is a rare example of a contemporary mathematician who has achieved outstanding results in two quite different areas of research: algebra and probability. In both areas, his ideas constitute an essential part of modern mathematical knowledge and form a basis for further development. Although his last work in algebra was published in 1955, his contributions continue to influence current research in algebra and in the physics of elementary particles. His work in probability is part of both the historical and the modern development of the topic. This volume presents Dynkin's scientific contributions in both areas. Included are Commentary by recognized experts in the corresponding fields who describe the time, place, role, and impact of Dynkin's research and achievements. Biographical notes and the recollections of his students are also featured.
  

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Contents

Dynkin and Lie theory G M Seitz
3
Classification of simple Lie groups
23
Calculation of the coeffecients in the CampbellHausdorff formula
31
Introduction 246
43
Chapter 3 Some problems in the theory of linear representations of semi
58
Maximal subgroups of the classical groups 37
65
Irreducible subgroups of the unimodular group SL N with
84
Irreducible subgroups of the symplectic group SpN with
96
Markov processes and semigroups of operators
437
Strong Markov Processes with A A Yushkevich
449
Infinitesimal operators of Markov processes
455
The natural topology and excessive functions connected with a Markov
477
The optimum choice of the instant for stopping a Markov process
485
Diffusion of tensors
515
Determining functions of Markov processes and corresponding dual regular
525
Comments by I V Evstigneev
547

Supplement Survey of the basic concepts and facts in the theory of lin
111
Comments by A L Onishchik
171
Comments by A L Onishchik
309
Topological characteristics of homomorphisms of compact Lie groups
317
Bibliography
358
Comments by A L Onishchik
359
Tables
364
Comments on the impact of Dynkins work on current research
365
Lie groups in physics K Gottfried
371
Introduction
374
Dynkin and probability theory A A Yushkevich
385
Necessary and sufficient statistics for a family of probability distributions
393
Some limit theorems for sums of independent random variables with infinite
417
Greens and Dirichlet spaces associated with fine Markov processes
577
Markov processes as a tool in field theory
615
Symmetric statistics Poisson point processes and multiple Wiener integrals
637
Gaussian and nonGaussian random fields associated with Markov processes
645
An application of flows to time shift and time reversal in stochastic
675
Authors comments
683
A probabilistic approach to one class of nonlinear differential equations
711
Superdiffusions and parabolic nonlinear differential equations 739
761
To the history of strong Markov property A A Yushkevich
773
On compactifications of symmetric spaces M A Olshanetsky 111
781
Dynkins work in mathematical economics I V Evstigneev
793
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