Gamkrelidze Mathematical Analysis

Erscheinungsjahr 2012
ISBN: 978-1-4684-3303-6
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 8, 215 Seiten, eBook

Reihe: Progress in Mathematics

This volume contains three articles: "Asymptotic methods in the theory of ordinary differential equations" b'y V. F. Butuzov, A. B. Vasil'eva, and M. V. Fedoryuk, "The theory of best ap proximation in Dormed linear spaces" by A. L. Garkavi, and "Dy namical systems with invariant measure" by A. 'VI. Vershik and S. A. Yuzvinskii. The first article surveys the literature on linear and non linear singular asymptotic problems, in particular, differential equations with a small parameter. The period covered by the survey is primarily 1962-1967. The second article is devoted to the problem of existence, characterization, and uniqueness of best approximations in Banach spaces. One of the chapters also deals with the problem of the convergence of positive operators, inasmuch as the ideas and methods of this theory are close to those of the theory of best ap proximation. The survey covers the literature of the decade 1958-1967. The third article is devoted to a comparatively new and rapid ly growing branch of mathematics which is closely related to many classical and modern mathematical disciplines. A survey is given of results in entropy theory, classical dynamic systems, ergodic theorems, etc. The results surveyed were primarily published during the period 1956-1967.

Zielgruppe

Research

Autoren/Hrsg.

Gamkrelidze, R. V.

Inhaltsverzeichnis

Asymptotic Methods in the Theory of Ordinary Differential Equations.- I: Linear Differential Equations.- II: Nonlinear Differential Equations.- The Theory of Best Approximation in Normed Linear Spaces.- I. Best Approximation by Polynomials and Their Generalization in Classical Function Spaces.- II. The Problem ol Best Approximation in Banach Spaces.- III. Geometric Problems in the Theory of Best Approximation.- IV. On the Approximation of Sets.- V. On the Convergence of Positive Linear Operators.- Dynamical Systems with Invariant Measure.- 1. Introduction.- 2. Entropy Theory.- 3. Spectral Theory and Operator Rings.- 4. Ergodic Theorems.- 5. Classical Systems.- 6. Systems of Algebraic and Number-Theoretic Extraction.- 7. Transformations with Infinite and Quasi-Invariant Measure and the Existence of an Invariant Measure.- 8. Other Questions.