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Selected Research Papers
Among the finest achievements in modern mathematics are two of L.S. Pontryagin's most notable contributions: Pontryagin duality and his general theory of characters of a locally compact commutative group. This book, the first in a four-volume set, contains the most important papers of this eminent mathematician, those which have influenced many generations of mathematicians worldwide. They chronicle the development of his work in many areas, from his early efforts in homology groups, duality theorems, and dimension theory to his later achievements in homotopic topology and optimal control theory.
Principles of Optimal Control Theory
In the late 1950's, the group of Soviet mathematicians consisting of L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko made fundamental contributions to optimal control theory. Much of their work was collected in their monograph, The Mathematical Theory of Optimal Processes. Subsequently, Professor Gamkrelidze made further important contributions to the theory of necessary conditions for problems of optimal control and general optimization problems. In the present monograph, Professor Gamkrelidze presents his current view of the fundamentals of optimal control theory. It is intended for use in a one-semester graduate course or advanced undergraduate course. We are ...
Selected Research Papers
Among the finest achievements in modern mathematics are two of L.S. Pontryagin's most notable contributions: Pontryagin duality and his general theory of characters of a locally compact commutative group. This book, the first in a four-volume set, contains the most important papers of this eminent mathematician, those which have influenced many generations of mathematicians worldwide. They chronicle the development of his work in many areas, from his early efforts in homology groups, duality theorems, and dimension theory to his later achievements in homotopic topology and optimal control theory. On 3 September 1983 Lev Semenovich Pontryagin was seventy-five. To mark this important event in ...
Mathematical Analysis
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 al...
Some Questions in the Theory of Oscillations and the Theory of Optimal Control
This book contains two fundamental papers. The first is, in essence, a short monograph devoted to the theory of periodic motions in singularly perturbed systems. The second deals with structural properties of the solutions of a system having infinitely many switchings on a finite time interval to Hamiltonian systems with discontinuous right-hand side.
Selected Research Papers
Among the finest achievements in modern mathematics are two of L.S. Pontryagin's most notable contributions: Pontryagin duality and his general theory of characters of a locally compact commutative group. This book, the first in a four-volume set, contains the most important papers of this eminent mathematician, those which have influenced many generations of mathematicians worldwide. They chronicle the development of his work in many areas, from his early efforts in homology groups, duality theorems, and dimension theory to his later achievements in homotopic topology and optimal control theory.
Analysis I
Infinite series, and their analogues-integral representations, became fundamental tools in mathematical analysis, starting in the second half of the seventeenth century. They have provided the means for introducing into analysis all o( the so-called transcendental functions, including those which are now called elementary (the logarithm, exponential and trigonometric functions). With their help the solutions of many differential equations, both ordinary and partial, have been found. In fact the whole development of mathematical analysis from Newton up to the end of the nineteenth century was in the closest way connected with the development of the apparatus of series and integral representat...
Algebra and Geometry
This volume contains five review articles, three in the Al gebra part and two in the Geometry part, surveying the fields of ring theory, modules, and lattice theory in the former, and those of integral geometry and differential-geometric methods in the calculus of variations in the latter. The literature covered is primarily that published in 1965-1968. v CONTENTS ALGEBRA RING THEORY L. A. Bokut', K. A. Zhevlakov, and E. N. Kuz'min § 1. Associative Rings. . . . . . . . . . . . . . . . . . . . 3 § 2. Lie Algebras and Their Generalizations. . . . . . . 13 ~ 3. Alternative and Jordan Rings. . . . . . . . . . . . . . . . 18 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
