Friedrich Moritz Hartogs

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Friedrich Hartogs

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

Life

Hartogs was born as the son of the businessman Gustav Hartogs and his wife Elise Feist and grew up in Frankfurt am Main . He studied at the Technical University of Hanover , at the Technical University and the University of Berlin as well as at the Ludwig Maximilians University in Munich , where he received his doctorate with distinction in 1903 under Alfred Pringsheim .

After his habilitation in 1905 he was a private lecturer, in 1910 an extraordinary (1912 "regular" extraordinary) and in 1927 a full professor in Munich. His election to the Bavarian Academy of Sciences failed, however, because a chemist was preferred. One reason for his "career delays" was his z. B. in the memories of André Weil testified to shy and reserved nature. He turned down a call to the University of Frankfurt in 1922 because he was too uncertain about the university's foundation status in times of inflation. In 1935 he was dismissed as a Jew by the National Socialists (he was not dismissed as early as 1933, as he was a civil servant before 1914). In 1938, after the pogroms of the Reichspogromnacht, he was briefly sent to the Dachau concentration camp and abused. In 1941 he had to wear the Star of David; However, he was initially able to avert admission to a labor camp through a divorce process agreed with his non-Jewish wife, thus avoiding the impending expropriation of his house. In 1943, tired of the constant humiliation and in view of his impending arrest (the local group leader of the NSDAP from Pullach seemed to have tacitly tolerated his stay until then), he committed suicide with an overdose of sleeping pills. His wife, whom he married in 1900, and his four children (three of them abroad) survived the war.

plant

Hartogs pioneered complex multi-variable analysis. A theorem by Hartogs (in his habilitation in 1905) ensures the holomorphism of functions of several variables if they are holomorphic in each variable separately. In particular, they are also continuous, in contrast to the relationships in the real case. The continuity set of Hartog (or lemma Hartog ) represents the continuation of holomorphic functions of several variables, holomorphic in the vicinity of the associated (connected) edge of a limited area K of the ( n > 1) in K in safely. Hartogs formulated and proved the theorem for special areas K and special environments. For example, he proved the holomorphic continuability of a holomorphic function on an open spherical shell into the interior of the sphere, where, in contrast to a variable, no isolated singularities can exist. In his thesis, he proved continuability a in the vicinity of a cylinder K holomorphic in two dimensions complex function in K inside. The basic terms holomorphic envelope and holomorphic area later emerged from this work .

In the set theory is set of Hartog known of the existence of a well-ordered set larger at any amount cardinality ensures. In addition, in his 1915 essay he gave a new proof of the Zermelos well-order theorem using the principle of comparability of cardinalities ( trichotomy ) instead of the axiom of choice (it follows that trichotomy is equivalent to the axiom of choice). In 1909 he gave an elementary proof of Weierstrasse's preparatory theorem . In 1925 he gave a new proof of Jordan's curve theorem .

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