Bøger i Springer Collected Works in Mathematics serien

Published with the Cooperation of the Institute of Mathematical Statistics

Luis Santalo was a mathematician who laid the foundations of Stereology and its applications. This book contains a selection of his papers as well as a short biography, photographs, a list of his publications, and various appreciations of his influence.

Covering a period up to 1971, this selection of Saunders Mac Lane's most distinguished papers takes the reader on a journey through the most important milestones of the mathematical world in the twentieth century. Later, he contributed to the more abstract and general mathematical viewpoints which emerged in the twentieth century.

The creative work of Andrei N. Kolmogorov is exceptionally wide-ranging. In his studies on trigonometric and orthogonal series, the theory of measure and inte­gral, mathematical logic, approximation theory, geometry, topology, functional analysis, classical mechanics, ergodic theory, superposition of functions, and in­ formation theory, he solved many conceptual and fundamental problems and posed new questions which gave rise to a great deal of further research. Kolmogorov is one of the founders of the Soviet school of probability theory, mathematical statistics, and the theory of turbulence. In these areas he obtained a number of central results, with many applications to mechanics, geophysics, linguistics and biology, among other subjects. This edition includes Kolmogorov's most important papers on mathematics and the natural sciences. It does not include his philosophical and ped­agogical studies, his articles written for the "Bolshaya Sovetskaya Entsiklopediya", his papers on prosody and applications of mathematics or his publications on general questions. The material of this edition was selected and compiled by Kolmogorov himself.The first volume consists of papers on mathematics and also on turbulence and classical mechanics. The second volume is devoted to probability theory and mathematical statistics. The focus of the third volume is on information theory and the theory of algorithms.

The creative work of Andrei N. Kolmogorov is exceptionally wide-ranging. In his studies on trigonometric and orthogonal series, the theory of measure and inte­gral, mathematical logic, approximation theory, geometry, topology, functional analysis, classical mechanics, ergodic theory, superposition of functions, and in­ formation theory, he solved many conceptual and fundamental problems and posed new questions which gave rise to a great deal of further research. Kolmogorov is one of the founders of the Soviet school of probability theory, mathematical statistics, and the theory of turbulence. In these areas he obtained a number of central results, with many applications to mechanics, geophysics, linguistics and biology, among other subjects. This edition includes Kolmogorov's most important papers on mathematics and the natural sciences. It does not include his philosophical and ped­agogical studies, his articles written for the "Bolshaya Sovetskaya Entsiklopediya", his papers on prosody and applications of mathematics or his publications on general questions. The material of this edition was selected and compiled by Kolmogorov himself.The first volume consists of papers on mathematics and also on turbulence and classical mechanics. The second volume is devoted to probability theory and mathematical statistics. The focus of the third volume is on information theory and the theory of algorithms.

Dealing with functional analysis, real analysis and hydrodynamics, this second volume features commentaries written by Wilhelm Frank, Davis Preiss, and Alfred Kluwick.

Presents a collection of Hahn's writings on harmonic analysis, measure and integration, complex analysis and philosophy, which are commented upon by Jean-Pierre Kahane, Heinz Bauer, Lutger Kaup, and Christian Thiel. This volume also contains excerpts of letters of Hahn and accounts by students and colleagues.

From the Preface by V. S. VARADARAJAN: ¿These volumes of the Collected Papers of Harish-Chandra are being brought out in response to a widespread feeling in the mathematical community that they would immensely benefit scholars and research workers, especially those in analysis, representation theory, arithmetic, mathematical physics, and other related areas. lt is hoped that in addition to making his contributions more accessible by collecting them in one place, these volumes would help focus renewed attention on his ideas and methods as well as lend additional perspective to them.¿ The papers are arranged chronologically, Volume I collects Harish-Chandra's articles written between 1944 and 1954.