Books in the Springer Collected Works in Mathematics series

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.

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

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.

Aus dem Vorwort: "Die Ergebnisse, Methoden und Begriffe, die die mathematische Wissenschaft dem Forscher ISSAI SCHUR verdankt, haben ihre nachhaltige Wirkung bis in die Gegenwart hinein erwiesen und werden sie unverändert beibehalten. Immer wieder wird auf Unter­suchungen von SCHUR zurückgegriffen, werden Erkenntnisse von ihm benutzt oder fortgeführt und werden Vermutungen von ihm bestätigt... Die Besonderheit des mathematischen Schaffens von SCHUR hat einst MAX PLANCK, als Sekretär der physikalisch-mathematischen Klasse der Preußischen Akademie der Wissenschaften zu Berlin, gut gekennzeichnet. In seiner Erwiderung auf die Antrittsrede von SCHUR bei dessen Aufnahme als ordentliches Mitglied der Akademie am 29. Juni 1922 bezeugte er, daß SCHUR "wie nur wenige Mathematiker die große Abelsche Kunst übe, die Probleme richtig zu formulieren, passend umzuformen, geschickt zu teilen und dann einzeln zu bewältigen"."Band III enthält 28 von Issai Schur verfasste Artikel ab 1925 sowie u.a.Inhalte aus dem nicht veröffentlichten Nachlass.

Mumford is a well-known mathematician and winner of the Fields Medal, the highest honor available in mathematics. Many of these papers are currently unavailable, and the commentaries by Gieseker, Lange, Viehweg and Kempf are being published here for the first time.

I.M. Gelfand (1913 - 2009), one of the world''s leading contemporary mathematicians, largely determined the modern view of functional analysis with its numerous relations to other branches of mathematics, including mathematical physics, algebra, topology, differential geometry and analysis. In this three-volume Collected Papers Gelfand presents a representative sample of his work. Gelfand''s research led to the development of remarkable mathematical theories - most of which are now classics - in the field of Banach algebras, infinite-dimensional representations of Lie groups, the inverse Sturm-Liouville problem, cohomology of infinite-dimensional Lie algebras, integral geometry, generalized functions and general hypergeometric functions. The corresponding papers form the major part of the collection. Some articles on numerical methods and cybernetics as well as a few on biology are also included. A substantial number of the papers have been translated into English especially for this edition. The collection is rounded off by an extensive bibliography with almost 500 references. Gelfand''s Collected Papers will be a great stimulus, especially for the younger generation, and will provide a strong incentive to researchers.

This book collects 20 papers that span the areas of mathematical physics, dynamical systems, and probability. Yakov Sinai is well-known as both a mathematician and a physicist, with numerous theorems and proofs bearing his name in both fields.

"These volumes collect almost all of the research and expository papers of J.-P. Serre published in mathematical journals through 1984, as well as some of his seminar reports, and a few items not previously published. .... Throughout his writings, Serre has liberally sprinkled open questions and conjectures. Most endnotes list subsequent progress made on these questions or improvements to the main results of the papers. Some make additional comments, and a few are corrections. These endnotes alone justify the publication of the collected works. Serre is one of the masters of mathematical exposition...." --James Milne, University of Michigan, in Math Reviews

These articles span the years from 1961-1980 while David Mumford was an active researcher in the area of algebraic geometry. This volume includes many important papers previously omitted. Mumford's correspondence with Grothendieck is also included.

Karl Menger, one of the founders of dimension theory, is among the most original mathematicians and thinkers of the twentieth century.

Karl Menger, one of the founders of dimension theory, is among the most original mathematicians and thinkers of the twentieth century.

, "Uber die analytische Methoden in der Wahrscheinlichkeitsrechnung," Math Ann. , "Zur Theorie der stochastischen Prozesse," Math Ann. , "Stochastic processes depending on a continuous parameter, " TAMS 42 (1937)) still appeared impregnable to all but the most erudite.