Descriptive Theory of Sets And Functions: Functional Analysis in Semi-ordered Spaces - Couverture rigide

Kantorovich, L.V.

Couverture rigide

ISBN 10 : 2884490124 ISBN 13 : 9782884490122

Editeur : Gordon & Breach Science Publishers Ltd, 1996

Synopsis

This book presents articles of L.V. Kantorovich on the descriptive theory of sets and function and on functional analysis in semi-ordered spaces, to demonstrate the unity of L.V. Kantorovich's creative research. It also includes two papers on the "extension of Hilbert space".

A propos du livre

Présentation de l'éditeur

Part I of the Selected Works of L.V.Kantorovich is devoted to his mathematical work, with particular emphasis on the contribution he made to set theory and methods of mathematical approximation. The book begins with some chapters on the Descriptive Theory of Sets and Real Functions. Topics include universal functions, W.H. Young's classification, generalized derivatives of continuous functions and the H. Steinhaus problem. The book also includes papers on functional analysis in semi-ordered vector spaces, as well as articles relevant to the extension of Hilbert space in the spirit of distribution theory. This indispensable reference provides a record of the achievements of a man whose originality and diversity of thought distinguished him as a remarkable mathematician. Kantorovich was a true polymath, whose mathematical work had applications across a very broad field of subjects, particularly economics. This book will prove to be a useful reference work for anyone interested in learning about the origin of a number of important mathematical ideas.

Part II of this set contains his works on Functional Analysis. The author deals with a number of approximate calculations and solutions including a discussion of an approximate calculation of certain types of definite integrals, and also a method for the approximate solution of partial differential equations. In addition to this, the author looks at various other methods, including the Ritz method, the Galerkin method in relation to the reduction of differential equations, and the Newton method for functional equations. Towards the end of the book there are several chapters on computers-a very early insight into what proved to be a development of enormous importance in the later half of the 20th century.
Kantorovich is often said to be the founding father of mathematical programming. His ideas of the 1930s, which could never to come to fruition in Stalin's Soviet Union, were later developed by other scientists, and have had a considerable impact on the world, particularly in the field of economics. This book will appeal to anyone seeking further insight into the works of this great mathematician.

Biographie de l'auteur

Leonid Vitalievich Kantorovich was born in St Petersburg in 1912, and embarked upon a life's work in mathematics at an early age, writing his first book at the age of 21, and gaining a professorship at Leningrad State University a year later. During the course of his life he wrote numerous mathematical books and articles and was recognised by many foreign universities and institutes. In 1975 he was awarded the Nobel Memorial Prize for economics together with T.C. Koopmans for their joint contribution to the theory of optimum allocation of resources. Up until his death in 1986, Kantorovich remained a respected figure in the world of applied mathematics, and his works proved to be influential across a wide range of disciplines.

Détails de l'édition

• Éditeur: Gordon & Breach Science Publishers Ltd
• Date d'édition: 1996
• ISBN 10: 2884490124
• ISBN 13: 9782884490122
• Reliure: Relié
• Langue: anglais
• Nombre de pages: 376
• Coordonnées du fabricant: non disponible