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基本説明
The list selected is very representative both topically and geographically. Most of the work presented in this volume was done during the Soviet era.
Full Description
In the 20th century, many mathematicians in Russia made great contributions to the field of mathematics. This invaluable book, which presents the main achievements of Russian mathematicians in that century, is the first most comprehensive book on Russian mathematicians. It has been produced as a gesture of respect and appreciation for those mathematicians and it will serve as a good reference and an inspiration for future mathematicians. It presents differences in mathematical styles and focuses on Soviet mathematicians who often discussed "what to do" rather than "how to do it". Thus, the book will be valued beyond historical documentation.The editor, Professor Yakov Sinai, a distinguished Russian mathematician, has taken pains to select leading Russian mathematicians — such as Lyapunov, Luzin, Egorov, Kolmogorov, Pontryagin, Vinogradov, Sobolev, Petrovski and Krein — and their most important works. One can, for example, find works of Lyapunov, which parallel those of Poincaré; and works of Luzin, whose analysis plays a very important role in the history of Russian mathematics; Kolmogorov has established the foundations of probability based on analysis. The editor has tried to provide some parity and, at the same time, included papers that are of interest even today.The original works of the great mathematicians will prove to be enjoyable to readers and useful to the many researchers who are preserving the interest in how mathematics was done in the former Soviet Union.
Contents
Lyapunov (A New Case of Integrability of Differential Equations of Motion of a Solid Body in Liquid); Luzin (Sur l'absolue convergence des series trigonometriques); Steklov; Egorov (Mathematics and Religion in Moscow, by C E Ford); Smirnov (Sur les polynomes orthogonaux a une veriable complexe); Bernstein (Sur la meilleure approximation sur tout l'axe reel des fonctions continues par des fonctions entieres de degre fini); Urysohn; Chebotaryov; Vinogradov (Representation of an Odd Number as the Sum of Three Primes); Aleksandrov (Sur la notion de dimension des ensembles fermes); Menshov; Gelfond (Sur le septierie probleme de Hilbert); Khinchin (Three Pearls of Number Theory); Kolmogorov (Local Structure of Turbulence in an Incompressible Viscous Fluid at Very Large Reynolds Numbers); Pontryagin (Homotopic Classification of an (n+2)-Dimensional Spheres into an n-Dimensional Spheres); Gelfand (On Identities for Eigenvalues of a Second Order Differential Operators); Sobolev (On a Theorem of Functional Analysis); Petrovsky (On Problem of some PDE's); Krein (On Extreme Points of Regularly Convex Sets); Liusternik (Topology and Variational Problem); Rokhlin (Proof of Gudkov's Hypothesis); Novikov (Periodic Groups); Bogoliubov (Mathematical Problems of Quantum Field Theory); Aleksandrov (Neue ungleichungen fur die mischvolumen konvexer korper); Kantorovich (A New Method of Solving of Some Classes of Extremal Problems); Malcev (Free Topological Algebras); Linnik (An Application of the Theory of Matrices and of Lobatschevskian Geometry to the Theory of Dirichlet's Real Characters); Markov (The Theory of Algorithms); Lavrentev (On the Theory of Quasi-Conformal Mapping of Three-Dimensional Domains); Tikhonov (Ueber die Erweiteung von Raumen); Delone (Sur le nombre de representations d'un nombre par une forme eubique a discriminent negatif); Keldysh (On the Completeness of the Eigenfunctions of Some Classes of Non-Self Adjoint Linear Operators); Faddeev; and other articles.
