Franz Rellich
From Wikipedia, the free encyclopedia
Franz Rellich (September 14, 1906–September 25, 1955) was a Austrian-Italian mathematician. He made important contributions in mathematical physics, in particular for the foundations of quantum mechanics and for the theory of partial differential equations.
Contents |
[edit] Biography
Rellich was born in Tramin (Termeno), Bolzano-Bozen. He studied from 1924 to 1929 at the universities of Graz and Göttingen and received his doctor's degree in 1929 under Richard Courant at Georg August University of Göttingen with the thesis about "Verallgemeinerung der Riemannschen Integrationsmethode auf Differentialgleichungen n-ter Ordnung in zwei Veränderlichen" ("Generalization of Riemann's integration method on differential equations of n-th order in two variables"). When in 1933 the great mathematical-physical tradition in Göttingen terminated with the Machtergreifung of the Nazis, among others Rellich had to leave, having taken an active position against nazism. In 1934 he became Privatdozent in Marburg, in 1942 professor in Dresden, and in 1946 director of the Mathematical Institute in Göttingen, being instrumental in its reconstruction. Jürgen Moser was one of his students. Rellich died in Göttingen.
[edit] Contributions
Among his most important mathematical contributions are his works in perturbation theory of linear Operators in Hilbert space, considering the dependence of the spectral family 
of a self-adjoint operator 
in Hilbert space on the parameter 
. Although this problem originated from quantum mechanics and is again applied to quantum mechanics, his considerations were completely abstract.
Rellich successfully worked on many partial differential equations with degeneracies. For instance, he showed that the Monge-Ampère differential equation in the elliptic case, where it is not necessarily uniquely soluble, can have at most two solutions.
From the physical point of view, Rellich's mathematical clarification of the outgoing Sommerfeld conditions were relevant. In 1940 he proved the fact now known as Rellich's Theorem that a differential equation w′ = f(z, w) has at most countably many entire solutions w(z), if f(z, w) is a linear entire function in w.
[edit] Sources
- Biographical notes by Göttingen University (in German)
- S. Gottwald, H.-J. Ilgauds, K.-H. Schlote (Hrsg.): Lexikon bedeutender Mathematiker. Verlag Harri Thun, Frankfurt a. M. 1990 ISBN 3-8171-1164-9
