Franz Rellich (September 14, 1906 – September 25, 1955) was an

Austrian Austrian may refer to: * Austrians, someone from Austria or of Austrian descent ** Someone who is considered an Austrian citizen, see Austrian nationality law * Austrian German dialect * Something associated with the country Austria, for example: ...

German German(s) may refer to: * Germany (of or related to) **Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ger ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He made important contributions in

mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...

, in particular for the foundations of

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

and for the theory of

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s. The

Rellich–Kondrachov theorem In mathematics, the Rellich–Kondrachov theorem is a compact embedding theorem concerning Sobolev spaces. It is named after the Austrian-German mathematician Franz Rellich and the Russian mathematician Vladimir Iosifovich Kondrashov. Rellich pr ...

is named after him.

Biography

Rellich was born in Tramin, then in the

County of Tyrol The (Princely) County of Tyrol was an estate of the Holy Roman Empire established about 1140. After 1253, it was ruled by the House of Gorizia and from 1363 by the House of Habsburg. In 1804, the County of Tyrol, unified with the secularised pr ...

. He studied from 1924 to 1929 at the universities of

Graz Graz (; sl, Gradec) is the capital city of the Austrian state of Styria and second-largest city in Austria after Vienna. As of 1 January 2021, it had a population of 331,562 (294,236 of whom had principal-residence status). In 2018, the popul ...

and

Göttingen Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...

and received his doctor's degree in 1929 under

Richard Courant Richard Courant (January 8, 1888 – January 27, 1972) was a German American mathematician. He is best known by the general public for the book '' What is Mathematics?'', co-written with Herbert Robbins. His research focused on the areas of real ...

Georg August University of Göttingen Georg may refer to: * ''Georg'' (film), 1997 *Georg (musical), Estonian musical * Georg (given name) * Georg (surname) * , a Kriegsmarine coastal tanker See also * George (disambiguation) George may refer to: People * George (given name) * G ...

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 Adolf Hitler's rise to power began in the newly established Weimar Republic in September 1919 when Hitler joined the '' Deutsche Arbeiterpartei'' (DAP; German Workers' Party). He rose to a place of prominence in the early years of the party. Be ...

'' of the

Nazis Nazism ( ; german: Nazismus), the common name in English for National Socialism (german: Nationalsozialismus, ), is the far-right totalitarian political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Na ...

, Rellich, having taken an active position against Nazism, was among those forced to leave. In 1934 he became ''

Privatdozent ''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualific ...

'' in

Marburg Marburg ( or ) is a university town in the German federal state (''Bundesland'') of Hesse, capital of the Marburg-Biedenkopf district (''Landkreis''). The town area spreads along the valley of the river Lahn and has a population of approximate ...

, in 1942 professor in

Dresden Dresden (, ; Upper Saxon: ''Dräsdn''; wen, label=Upper Sorbian, Drježdźany) is the capital city of the German state of Saxony and its second most populous city, after Leipzig. It is the 12th most populous city of Germany, the fourth larg ...

, and in 1946 director of the Mathematical Institute in Göttingen, being instrumental in its reconstruction.

Erhard Heinz Erhard Heinz (30 April 1924, Bautzen – 29 December 2017, Göttingen) was a German mathematician known for his work on partial differential equations, in particular the Monge–Ampère equation. He worked as professor in Stanford, Munich and from ...

, Konrad Jörgens, and

Jürgen Moser Jürgen Kurt Moser (July 4, 1928 – December 17, 1999) was a German-American mathematician, honored for work spanning over four decades, including Hamiltonian dynamical systems and partial differential equations. Life Moser's mother Ilse Strehl ...

were among of his doctoral students. His sister Camilla Juliana Anna was the wife of mathematician

Bartel Leendert van der Waerden Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch mathematician and historian of mathematics. Biography Education and early career Van der Waerden learned advanced mathematics at the University of Amsterd ...

. Rellich died in

Contributions

Among Rellich's most important mathematical contributions are his work in the

perturbation theory In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle ...

linear operator In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that pre ...

s on

Hilbert space In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise natural ...

s: he studied the dependence of the spectral family

E_\varepsilon(\lambda)

of a

self-adjoint operator In mathematics, a self-adjoint operator on an infinite-dimensional complex vector space ''V'' with inner product \langle\cdot,\cdot\rangle (equivalently, a Hermitian operator in the finite-dimensional case) is a linear map ''A'' (from ''V'' to itse ...

A_\varepsilon

on the parameter

\varepsilon

. Although the origins and applications of the problem are in

, Rellich's approach was completely abstract. Rellich successfully worked on many

s with degeneracies. For instance, he showed that in the elliptic case, the Monge-Ampère differential equation, while not necessarily uniquely soluble, can have at most two solutions. Particularly relevant to physics was Rellich's mathematical clarification of the outgoing

Sommerfeld Arnold Johannes Wilhelm Sommerfeld, (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretica ...

conditions.

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

External links

* * {{DEFAULTSORT:Rellich, Franz 1906 births 1955 deaths 20th-century Austrian mathematicians University of Göttingen alumni Academic staff of the University of Göttingen Mathematical physicists Austro-Hungarian mathematicians People from Tramin an der Weinstraße Austrian emigrants to Germany