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