Title | Mathematical Analysis [electronic resource] / edited by R. V. Gamkrelidze |
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Imprint | Boston, MA : Springer US : Imprint: Springer, 1970 |

Connect to | http://dx.doi.org/10.1007/978-1-4684-3303-6 |

Descript | VIII, 215 p. online resource |

SUMMARY

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 apยญ proximation in Dormed linear spaces" by A. L. Garkavi, and "Dyยญ namical systems with invariant measure" by A. 'VI. Vershik and S. A. Yuzvinskii. The first article surveys the literature on linear and nonยญ 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 apยญ proximation. The survey covers the literature of the decade 1958-1967. The third article is devoted to a comparatively new and rapidยญ 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

CONTENT

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

Mathematics
Algebra
Mathematical analysis
Analysis (Mathematics)
Mathematics
Analysis
Algebra