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Kolmogorov's Heritage in Mathematics.

Author: Eric Charpentier; Nikolai Nikolski
Publisher: Dordrecht : Springer, 2007.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject. Most mathematicians  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Eric Charpentier; Nikolai Nikolski
ISBN: 9783540363514 3540363513 128106727X 9781281067272
OCLC Number: 437205538
Description: 1 online resource (328 p.)
Contents: Front Matter; The youth of Andrei Nikolaevich and Fourier series; Kolmogorov's contribution to intuitionistic logic; Some aspects of the probabilistic work; Infinite dimensional Kolmogorov equations; From Kolmogorov's theorem on empirical distribution to number theory; Kolmogorov's e-entropy and the problem of statistical estimation; Kolmogorov and topology; Geometry and approximation theory in A.N. Kolmogorov's works; Kolmogorov and population dynamics; Resonances and small divisors; The KAM Theorem; From Kolmogorov's Work on entropy of dynamical systems to Non-uniformly hyperbolic dynamics. From Hilbert's 13th Problem to the theory of neural networks: constructive aspects of Kolmogorov's Superposition TheoremKolmogorov Complexity; Algorithmic Chaos and the Incompressibility Method.

Abstract:

A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject. Most mathematicians prove what they can, Kolmogorov was of those who prove what they want. For this book several world experts were asked to present one part of the mathematical heritage left to us by K.

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