Ernst Sigismund Fischer


Quick Info

Born
12 July 1875
Vienna, Austria
Died
14 November 1954
Cologne, Germany

Summary
Ernst Fischer is best known for the Riesz-Fischer theorem in the theory of Lebesgue integration.

Biography

Ernst Fischer's father was Jacob Fischer who was a composer of music and Professor at the world famous Vienna Academy. His mother was Emma Grädener, the daughter of the musician Karl Grädener. Ernst was educated in Vienna, and he studied at the University of Vienna under from 1894. His doctoral studies were supervised by and he was awarded his doctorate by the University of Vienna in 1899. He spent 1899 at the University of Berlin, then studied at Zürich and Göttingen with . From 1902 he was assistant to E Waelsch at the German Technische Hochschule of Brünn (now Brno), becoming a there in 1904, then an extraordinary professor in 1910.

From 1911 until 1920, Fischer was professor at the University of Erlangen, appointed to fill the chair left vacant in the previous year when retired. had been awarded her doctorate from the University of Erlangen in 1907 having worked under 's supervision. When Fischer arrived in Erlangen it was natural for to work with him. After 's death in 1935, gave an address at which he spoke of Fischer's influence:-
Fischer's field was algebra ..., in particular the theory of elimination and of invariants. He exerted upon , I believe, a more penetrating influence than did. Under his direction the transition from 's formal standpoint to the method of approach was accomplished. She refers in her papers at this time again and again to conversations with Fischer.

Fischer is best known for one of the highpoints of the theory of integration, called the -Fischer Theorem. The theorem is that the space of all square-integrable functions is complete, in the sense that is complete, and the two spaces are isomorphic by means of a mapping based on a complete orthonormal system.
Fischer took part in World War I from 1915 to 1918. He married Ellis Strauss, the daughter of Pfarrers Eugen Strauss, in Erlangen in 1917. Fischer was 42 years old, his wife being 26; they had one daughter. From 1920 Fischer worked at the University of Cologne, remaining there until he retired in 1938.

Let us note again the major result, the -Fischer Theorem, for which he is best known as noted in the above quote. In 1907 Ernst Fischer studied orthonormal sequences of functions and gave necessary and sufficient conditions for a sequence of constants to be the of a square integrable function. His two papers of 1907 were Sur la convergence en moyenne and Applications d'un théorèm sur la convergence en moyenne both published in Comptes rendus of the Academy of Sciences in Paris. This work led to the concept of a space. published a similar result in the same year. The theorem, now called the -Fischer theorem, is one of the great achievements of the theory of integration.

Fischer went on to study , publishing his results in 1908 in the Archiv der Mathematik und Physik, and determinants, publishing a paper in 's Journal in the following year. He also published in the Problem and on finite abelian groups.


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Written by J J O'Connor and E F Robertson
Last Update August 2006