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Selected Papers of E. B. Dynkin with Commentary
Edited by: A. A. Yushkevich, University of North Carolina, Charlotte, NC, G. M. Seitz, University of Oregon, Eugene, OR, and A. L. Onishchik, Yaroslavl State University, Russia
A co-publication of the AMS and International Press.
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Collected Works
2000; 798 pp; hardcover
Volume: 14
ISBN-10: 0-8218-1065-0
ISBN-13: 978-0-8218-1065-1
List Price: US$148
Member Price: US$118.40
Order Code: CWORKS/14
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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.

This book is jointly published by the AMS and the International Press.

Readership

Graduate students and research mathematicians interested in algebra and probability.

Reviews

"This volume consists of six seminal papers by Dynkin on Lie groups and Lie algebras ... An especially valuable feature is the inclusion of comments and corrections for most of the papers by Dynkin and his colleagues."

-- Mathematical Reviews

Table of Contents

Part I: Lie groups and Lie algebras
  • G. M. Seitz -- Dynkin and Lie theory
  • F. I. Karpelevich, A. L. Onishchik, and E. B. Vinberg -- On the work of E. B. Dynkin in the theory of Lie groups
  • F. I. Karpelevich, A. L. Onishchik, and E. B. Vinberg -- Correction to On the work of E. B. Dynkin in the theory of Lie groups
  • E. B. Dynkin -- Classification of simple Lie groups
  • E. B. Dynkin -- Calculation of the coefficients in the Campbell-Hausdorff formula
  • E. B. Dynkin -- The maximal subgroups of the classical groups
  • A. L. Onishchik -- Comments on Maximal subgroups of the classical groups
  • E. B. Dynkin -- Semisimple subalgebras of semisimple Lie algebras
  • A. L. Onishchik -- Comments on the paper Semisimple subalgebras of semisimple Lie algebras
  • E. B. Dynkin -- Construction of primitive cycles in compact Lie groups
  • E. B. Dynkin -- Topological characteristics of homomorphisms of compact Lie groups
  • A. L. Onishchik -- Comments on the paper Topological characteristics of homomorphisms of compact Lie groups
  • B. Kostant -- Dynkin and modern Lie theory
  • D. A. Vogan, Jr. -- Comments on the impact of Dynkin's work on current research in representation theory
  • A. Gabrielov -- Coxeter-Dynkin diagrams and singularities
  • K. Gottfried -- Lie groups in physics
  • Y. Ne'eman -- Dynkin diagrams in the physics of particles, fields and strings
Part II: Probability theory
  • A. A. Yushkevich -- Dynkin and probability theory
  • E. B. Dynkin -- Necessary and sufficient statistics for a family of probability distributions
  • E. B. Dynkin -- Some limit theorems for sums of independent random variables with infinite mathematical expectations
  • E. B. Dynkin -- Markov processes and semigroups of operators
  • E. B. Dynkin and A. A. Yushkevich -- Strong Markov processes
  • E. B. Dynkin -- Infinitesimal operators of Markov processes
  • E. B. Dynkin -- The natural topology and excessive functions connected with a Markov process
  • E. B. Dynkin and M. B. Malyutov -- Random walk on groups with a finite number of generators
  • E. B. Dynkin -- The optimum choice of the instant for stopping a Markov process
  • E. B. Dynkin -- Brownian motion in certain symmetric spaces and nonnegative eigenfunctions of the Laplace-Beltrami operator
  • E. B. Dynkin -- Diffusion of tensors
  • E. B. Dynkin -- Game variant of a problem on optimal stopping
  • E. B. Dynkin and S. E. Kuznetsov -- Determining functions of Markov processes and corresponding dual regular classes
  • E. B. Dynkin -- Economic equilibrium under uncertainty
  • I. V. Evstigneev -- Comments on Economic equilibrium under uncertainty
  • E. B. Dynkin -- Markov processes and random fields
  • E. B. Dynkin -- Green's and Dirichlet spaces associated with fine Markov processes
  • E. B. Dynkin -- Markov processes as a tool in field theory
  • E. B. Dynkin and A. Mandelbaum -- Symmetric statistics, Poisson point processes, and multiple Wiener integrals
  • E. B. Dynkin -- Gaussian and non-Gaussian random fields associated with Markov processes
  • E. B. Dynkin -- Author's correction to Guassian and non-Gaussian random fields associated with Markov processes.
  • E. B. Dynkin -- An application of flows to time shift and time reversal in stochastic processes
  • E. B. Dynkin -- Author's comments on An application of flows to time shift and time reversal in stochastic processes
  • E. B. Dynkin -- Representation for functionals of superprocesses by multiple stochastic integrals, with applications to self-intersection local times
  • E. B. Dynkin -- A probabilistic approach to one class of nonlinear differential equations
  • E. B. Dynkin -- Superdiffusions and parabolic nonlinear differential equations
  • S. E. Kuznetsov -- Comments on Superdiffusions and parabolic nonlinear differential equations
  • P. A. Meyer -- Dynkin and the theory of Markov processes
  • A. A. Yushkevich -- To the history of strong Markov property
  • M. A. Olshanetsky -- On compactifications of symmetric spaces
  • J.-F. Le Gall -- Dynkin's contributions to superprocesses and partial differential equations
  • I. V. Evstigneev -- Dynkin's work in mathematical economics
  • Acknowledgments
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