Franz Rellich

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

Life

Rellich studied from 1924 to 1929 at the Universities of Graz and Göttingen and received his PhD in 1929 under Richard Courant at the Georg -August- University via a " generalization of the Riemann integration method for differential equations of order n in two variables ". When in 1933 the Göttingen mathematical-physical tradition was terminated after the Great Depression and the rise of the Nazis, had to go Rellich, who took an active stance against Nazism. In 1934 he became a lecturer in Marburg, 1942 Professor in Dresden and in 1946 director of the Mathematical Institute in Göttingen, on whose reconstruction he played an important part.

In 1950 he was invited speaker at the International Congress of Mathematicians (ICM ) in Cambridge (Massachusetts ) ( perturbation theory the spectral decomposition ), 1934 on the in Zurich (On the first boundary value problem for Monge - Ampère equations of elliptic type ) and 1954 in Amsterdam (half Restricted differential operators of higher order ).

Work

The greatest of his mathematical achievements are the work on the perturbation theory of linear operators in Hilbert space, in which he examined the dependence of the spectral function of a self-adjoint operator in the Hilbert space of the parameters. Although he applied this stemming from quantum mechanics question back to quantum mechanics, he continued his studies entirely abstract.

After Franz Rellich compactness theorem of Rellich - Kondratschow is named from the theory of Sobolev spaces.

Many partial differential equations, in which mathematical degenerations occur has treated Rellich successful. He shows, for example, that the Monge - Ampère equation in the elliptic case, where it is not necessary uniquely solvable, can have at most two solutions.

Physically was also important Rellichs mathematical clarification formulated by Arnold Sommerfeld radiation conditions.