Selected Papers of E. B. Dynkin with CommentaryAmerican Mathematical Soc., 2000 - 798 ページ 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. |
目次
Dynkin and Lie theory G M Seitz | 7 |
Classification of simple Lie groups | 17 |
Maximal subgroups of the classical groups | 23 |
Introduction 246 | 43 |
Some problems in the theory of linear representations of semi | 58 |
Irreducible subgroups of the unimodular group SLN with | 84 |
Irreducible subgroups of the symplectic group SpN with | 96 |
Irreducible subgroups of the orthogonal group 0N with | 100 |
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 |
Bibliography 362 | 154 |
Semisimple subalgebras of semisimple Lie algebras | 155 |
Comments by A L Onishchik | 313 |
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 |
Dynkins contributions to superprocesses and partial differential equations | 781 |
Dynkins work in mathematical economics I V Evstigneev | 793 |
多く使われている語句
A₁ A₂ adjoint adjoint representation Akad algebra G Appendix arbitrary Cartan subalgebra classification component conjugate contains Corollary corresponding decomposition defined denote diagram dimension distribution E. B. Dynkin elements equation equivalent extreme vector Feller process finite follows formula G₂ greatest vector greatest weight Hence idempotent inner automorphism integral invariant irreducible representation irreducible with respect isomorphic Lemma Let G Lie groups linear representation linear transformations mapping Markov processes Markov property Math matrices maximal subgroups measure necessary and sufficient obtained operator orthogonal positive probability problem Proof of Theorem proved reducible regular subalgebra relation representation of G Russian scheme semisimple algebra semisimple Lie algebras semisimple subalgebras simple algebra simple Lie algebras simple roots SL(N solution Sp(N space stochastic strong Markov subspace symmetric symplectic system of simple Table Theorem theory tion