Karl Stein (mathematician)

Karl Stein ( born January 1, 1913 in Hamm, † 19 October 2000 in Ebersbach an der Fils ) was a German mathematician. His area of ​​research was the complex analysis of several variables. The concept of Stein manifold goes back to him.

Life

Karl Stein studied from 1932 to 1936 at the Westfälische Wilhelms-Universität in Münster and Hamburg and Berlin and received his doctorate in 1937 with Heinrich Behnke. The title of his dissertation was the theory of functions of several complex variables; The Regularitätshüllen low-dimensional manifolds. In 1938, he was talking to a scholarship provided to Heidelberg. In 1940 he qualified as a professor in Münster.

During World War II he worked in the Chiffrierabteilung of the High Command of the Wehrmacht (director Erich Hüttenhain ), where he among other things, had to check the safety of German codes. He himself was responsible for the secretary and the Lorenz cipher machine, its employees Gisbert Hasenjaeger for Enigma. In 1946 he became a lecturer and later an adjunct professor in Münster. After a guest stay 1953/54, in Paris, he was appointed in 1955 at the Ludwig- Maximilians- University of Munich - the Chair Mathematics I, among other things, the previously Ferdinand von Lindemann and Constantin Carathéodory occupied. There he remained active on his retirement in 1981 also.

Work

In 1941 he is in his habilitation topological conditions for the solvability of Cousin problem. This involves the question of the existence of global analytic functions in several variables with given zero and Polstellenflächen. Stone here draws on work by the Japanese Kiyoshi Oka.

In 1951, he introduces shortly thereafter so designated by Henri Cartan and Jean -Pierre Serre Stein manifolds, a generalization of open Riemann surfaces in several complex dimensions. In the same year 1951 he developed with a geometric Behnke, oriented Riemann theory of complex spaces - about the same time as the more algebraic definition by Henri Cartan ( " analytic sets " ), the theory of stone with Reinhold Remmert expand in 1953. Hans Grauert and Remmert 1958 show the equivalence of both definitions.

Tributes

In 1990 he became the first mathematician Georg Cantor Medal awarded.

He was a member of the Bavarian Academy of Sciences, since 1970, a corresponding member of the Academy of Sciences in Göttingen and since 1982 the Austrian Academy of Sciences since 1962. In 1973 he received an honorary doctorate from the University of Münster. In 1966 he was president of the German Mathematical Society.

His doctoral students count Reinhold Remmert, Michael Schneider ( University of Bayreuth ), Otto Forster, Ivo Schneider and Martin Schottenloher.

Writings

• With Heinrich Behnke: On the theory of functions of several complex variables - The Regularitätshüllen low-dimensional manifolds. In: Math annals., 1937. Dissertation.
• With Heinrich Behnke: Analytic functions of several variables to predetermined zero and Polstellenflächen. In: Annual Report DMV. , 1937.
• With Heinrich Behnke: Convergent sequences of Regularitätsbereichen and Meromorphiekonvexität. In: Math annals., 1939.
• Topological conditions for the existence of analytic functions of complex variables at given zeros surfaces. In: Math annals. 1941/2. Habilitation.
• With Heinrich Behnke: Development of analytic functions on Riemann surfaces. In: Math annals. Band 120 1948.
• Analytic functions of several complex variables to set of periodicity and the second Cousin'sche problem. In: Math annals. Band123. In 1951.
• With Heinrich Behnke: modifications of complex manifolds and Riemannian areas. In: Math annals. 1951/2.
• With Reinhold Remmert: About the essential singularities of analytic sets. In: Math annals. In 1952.
• Analytical decompositions of complex spaces. In: Math annals. 1956/7.