Franz Rellich

Franz Rellich
(Photo from the Mathematical Research Institute Oberwolfach)

Franz Rellich (born September 14, 1906 in Tramin , † September 25, 1955 in Göttingen ) was a German mathematician from South Tyrol. He made important contributions in the context of mathematical physics , in particular for the fundamentals of quantum mechanics and for the theory of partial differential equations .

Life

Rellich studied from 1924 to 1929 at the Universities of Graz and Göttingen and received his doctorate in 1929 under Richard Courant at the Georg-August University on a "generalization of the Riemann integration method on differential equations of the nth order in two variables" . When in 1933 the Göttingen mathematical-physical tradition after the seizure of power was the Nazis ended, had to go Rellich that an active stance against the Nazis occupied. In 1934 he became a private lecturer in Marburg , in 1942 a professor in Dresden and in 1946 director of the Mathematical Institute in Göttingen, in whose reconstruction he played a key role.

In 1932 he was invited speaker at the International Congress of Mathematicians (ICM) in Zurich ( on the first boundary value problem in Monge-Ampère's differential equations of the elliptical type ), in 1950 at the one in Cambridge in Massachusetts ( perturbation theory of spectral decomposition ) and in 1954 in Amsterdam ( semi-bounded differential operators of higher order ).

In 1948 he was elected a full member of the Göttingen Academy of Sciences .

His estate is kept by the Central Archives of German Mathematicians' bequests at the Lower Saxony State and University Library in Göttingen .

His sister Camilla Juliana Anna was the wife of the mathematician Bartel Leendert van der Waerden .

plant

The most important of his mathematical achievements are the work on the perturbation theory of linear operators in Hilbert space , in which he investigated the dependence of the spectral family of a self-adjoint operator in Hilbert space on the parameter . Although he applied this question stemming from quantum mechanics again to quantum mechanics, he conducted his investigations in a completely abstract manner. ${\displaystyle E_{\varepsilon }(\lambda )}$ ${\displaystyle A_{\varepsilon }}$ ${\displaystyle \varepsilon }$

The compactness theorem by Rellich-Kondrachov from the theory of Sobolew spaces is named after Franz Rellich .

Rellich has also successfully treated many partial differential equations in which mathematical degeneracies occur. For example, he showed that the Monge-Ampère differential equation in the elliptical case, where it is not necessarily uniquely solvable, can have at most two solutions.

Rellich's mathematical clarification of the radiation conditions formulated by Arnold Sommerfeld was also physically important .

literature

• S. Gottwald, H.-J. Ilgauds, K.-H. Schlote (ed.): Lexicon of important mathematicians . Harri Thun publishing house, Frankfurt a. M. 1990, ISBN 3-8171-1164-9
• Richard Courant : Franz Rellich on memory , Mathematische Annalen 133, 1957, pp. 185–190
• Hubert Kalf :  Rellich, Franz. In: New German Biography (NDB). Volume 21, Duncker & Humblot, Berlin 2003, ISBN 3-428-11202-4 , p. 406 f. ( Digitized version ).

Web links

• Literature by Franz Rellich in the catalog of the German National Library
• Short biography on the website of the University of Göttingen
• JJ O'Connor, EF Robertson :  Franz Rellich. In: MacTutor History of Mathematics archive .
• Central archive of mathematicians' papers: Finding aid (PDF)

Individual evidence

1. ↑ Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 199.