Eberhard Hopf
Eberhard Frederich Ferdinand Hopf ( born April 4, 1902 in Salzburg, † July 24, 1983 in Bloomington (Indiana) ) was a German - American mathematician who contributed to the topology and ergodic theory of importance.
Curriculum vitae
Eberhard Hopf was born as the son of German merchant Friedrich Hopf in Salzburg, Austria. He received his high school diploma in 1920 at the Gymnasium in Berlin - Friedenau, began studying mathematics and physics at the University of Berlin in 1924 and studied for a semester in the same subjects at the University of Tübingen. He received his PhD 1925/1926 in Erhard Schmidt and Schur Isay and his habilitation in 1929 at the University of Berlin in mathematical astronomy.
1930 was Hopf scholarship from the Rockefeller Foundation, which enabled him to study classical mechanics at Harvard. During this time he worked on a number of mathematical and astronomical subjects. In particular, the publication On time average theorem in dynamics is considered by many to be the first well- to-understand work in modern ergodic theory. Another important contribution from this period is the Wiener-Hopf equation, which he developed in collaboration with Norbert Wiener; it is used in a discrete variant since about the 1960s extensively in communications engineering and geophysics.
With the support of Norbert Wiener Hopf 1931 Assistant Professor at the Mathematics Department of the Massachusetts Institute of Technology. Here he devoted himself mainly to ergodic theory. He distinguished himself during this time by his gift of explaining complex issues to colleagues and non-specialists easily understood. In this context, he also studied the behavior of geodesics on surfaces of negative curvature. Hopf made important contributions to the solution of the Navier -Stokes equations of hydrodynamics in two dimensions.
He returned in 1936 returned with his wife Ilse and his daughter Barbara to Germany when he was offered a professorship at the University of Leipzig. During this time he made ready the book Ergodic theory, which offers 81 pages for a succinct presentation of the topic. Due to the Second World War, he was obliged to work in 1942 at the German Research Institute for Gliding, who was charged with war major developments for the Air Force. At the initiative of Oskar Perron, 1944, he received a professorship at the University of Munich as successor Constantin Carathéodory.
At the invitation of Richard Courant, he went in 1947 to the United States, where he published the solution of the Hurewicz problem. He took U.S. citizenship in 1949 and worked as a professor at Indiana University, where he remained until his retirement in 1972.
Awards and honors
Hopf in 1971 awarded by the American Mathematical Society as Gibbs Lecturer. In 1981 he received the Leroy P. Steele Prize of the American Mathematical Society.
Writings
- Ergodic theory. Springer Verlag ( results of mathematics and its applications ), 1937, reprint 1970
- Collections of writings can be found inter alia in: A number of publications are available on the Göttingen Digitization Center online.
- Cathleen Synge Morawetz, James Serrin, Yakov Sinai: Selected Works of Eberhard Hopf with Commentaries. Oxford University Press, 2003, ISBN 082182077X