Friedrich Hartogs

Friedrich Moritz Hartogs, Fritz Hartogs, ( born May 20, 1874 in Brussels; † August 18, 1943 in Munich) was a German mathematician who is best known for his work on the theory of functions of several complex variables and to set theory.

Life

Hartog was born the son of businessman Gustav Hartog and his wife Elise Feist and grew up in Frankfurt am Main. He studied at the Technical University of Hannover, at the Technical University and the University of Berlin and the Ludwig -Maximilians- University of Munich, where Alfred Pringsheim he received his PhD in 1903 with honors.

After his habilitation in 1905 he was Associate Professor, 1910 Associate (1912 ' etat moderate " extraordinary ) and 1927 full professor in Munich. His choice of the Bavarian Academy of Sciences but failed because you preferred a chemist. One reason for his " Career delays " was his example shy and restrained in the memoirs of André Weil testified nature. A professor at the University of Frankfurt in 1922, he refused because he was too uncertain in times of inflation the foundation status of the university. In 1935, he was dismissed as a Jew by the Nazis ( a layoff in 1933 was accounted for, as he was before 1914 civil servants). In 1938 he was briefly trained and abused after the pogroms of Kristallnacht to Dachau concentration camp. In 1941, he had to wear the Jewish star, but an introduction to a labor camp, he could turn by a keeper with his non-Jewish wife divorce process first, so the threat of expropriation of his house was averted. In 1943 he committed to the constant humiliations tired and facing the threat of arrest ( the local leader of the NSDAP from Pullach seemed until then his stay to have condoned ) suicide with an overdose of sleeping pills. His wife, whom he married in 1900, and four children survived the war (three of them abroad).

Work

Hartogs did pioneering work in the field of complex analysis in several variables. A set of Hartogs ( In his habilitation in 1905), the holomorphy of functions of several variables sure if they are separately holomorphic in each variable. They are therefore in particular also continuously, in contrast to the situation in the real case. The continuity theorem of Hartogs (or lemma of Hartogs ) is the holomorphic continuation of functions of several variables, holomorphic in the contiguous area of the (continuous ) edge of a limited area of the K ( n> 1) in K into it safely. Hartogs formulated and proved the theorem for special areas K and specific environments. For example, he proved the holomorphic continuability a holomorphic on an open spherical shell functions to the ball inside, where as opposed to a variable thus can exist no isolated singularities. Already in his doctoral thesis he proved in the continuability one in the vicinity of a cylinder K holomorphic in two complex dimensions function in K. For these later works the basic concepts Holomorphiehülle and holomorphy emerged.

In set theory, the set of Hartogs is known, which ensures the existence of a well-ordered set of larger cardinality to each lot. In addition, he gave in his essay of 1915 a new proof of Zermelo's well-ordering theorem, using the principle of comparability of cardinalities instead of the axiom of choice ( this principle is equivalent to the axiom of choice ). In 1909 he gave an elementary proof of the Weierstrass preparation theorem. In 1925, he gave a new proof of the Jordan curve theorem.

Writings

• About the functions of several independent variables, Mathematische Annalen Volume 62, 1906, p 1
• Over recent studies in the field of analytic functions of several variables, Annual Report 1907 DMV
• About the problem of the well-ordering, Mathematische Annalen, Vol 76, 1915, p 438