Charles Loewner

from Wikipedia, the free encyclopedia
Charles Loewner (right) 1927

Charles Löwner , actually Karel Löwner, German also Karl Löwner, (born May 29, 1893 in Lana ; †  January 8, 1968 in Stanford , California ) was a Czech -American mathematician who mainly dealt with function theory and analysis .

Life

Löwner was born as the son of a Czech Jewish shop owner in Lana near Kladno and attended the German grammar school in Prague. In 1912 he began his studies at the German-speaking faculty of Charles University in Prague . At that time he called himself Karl Löwner in German spelling. In 1917 he received his doctorate there under Georg Pick in geometric function theory. He then worked as an assistant at the German Technical University in Prague before going to the University of Berlin in 1922 . There he rose to the position of private lecturer and in 1928 went to Cologne as an associate professor . In 1930 he went to Charles University in Prague, where he soon became a full professor. During the German invasion of Prague in 1939, he was imprisoned, but was able to leave the country with his wife and went to the USA, where John von Neumann gave him a teaching position at the University of Louisville . In 1944 he worked at Brown University on aerodynamic problems of importance to the war effort. In 1946 he went to Syracuse University and in 1951 as a professor at Stanford. He was known in Stanford for his clear and elegant lectures, his openness in discussions with students of all semesters and his problem seminar , where many students found ideas for their diploma and doctoral theses.

In 1923 Löwner proved a special case of the Bieberbach conjecture , which states that the nth coefficient in the power series expansion of a one-to-one function on the unit disk is not greater than n in terms of amount. Löwner proved the conjecture for the coefficient to be n = 3. The application of Löwner's differential equation discovered by him also formed the basis for the proof of the conjecture by Louis de Branges in 1985 .

Oded Schramm developed an idea from Löwner from his investigations into the Bieberbach conjecture (Löwner differential equation) for his " Schramm-Löwner-Evolutions " method (SLE) in stochastic geometry .

According to Löwner, the smallest ellipsoid in volume that contains a given compact set in Euclidean space is called the Löwner ellipsoid of this set. The name Löwner-John-Ellipsoid (not to be confused with the John-Ellipsoid ), which is also in use, is based on the in-depth results of Fritz John .

His PhD students included Lipman Bers (still in Prague), Adriano Garsia and Frank PM Pu.

See also

Fonts

  • Collected Papers , Birkhäuser 1988 (editor Lipman Bers)
  • Theory of continuous groups , MIT Press 1971, Dover Publ. 2008 (lecture, transcript based on Harley Flanders , Murray Protter )
  • Investigations into simple conformal images of the unit circle, I , Mathematische Annalen, Volume 89, 1923, pp. 103-121 (Löwner differential equation, case n = 3 of the Bieberbach conjecture), online

Web links

literature

Historical and biographical notes on Loewner in: Katz, Mikhail G .: Systolic geometry and topology. With an appendix by Jake P. Solomon. Mathematical Surveys and Monographs, 137. American Mathematical Society, Providence, RI, 2007. ISBN 978-0-8218-4177-8 (Chapter 2.2, pages 14-19)

Individual evidence

  1. ^ Robert Finn , Mitteilungen der DMV, Nachlass von Charles Loewner , Volume 17, 2009, Issue 1, p. 58, doi : 10.1515 / dmvm-2009-0024 (freely accessible)
  2. ↑ Löwner, Investigations into simple conformal images of the unit circle, I, Mathematische Annalen, Volume 89, 1923, pp. 103–121, online at DigiZeitschriften (freely accessible)
  3. ^ Friedrich Pukelsheim : Optimal Design of Experiments. Wiley 1993; Classics in Applied Mathematics 50, SIAM 2006, pp. 417, 428 online
  4. ^ Fritz John: Extremum problems with inequalities as subsidiary conditions. In: KO Friedrichs et al. (Ed.): Studies and essays, Courant Anniversary Volume. Interscience, New York 1948, pp. 187-204
  5. ^ Mathematics Genealogy Project
personal data
SURNAME Loewner, Charles
ALTERNATIVE NAMES Lowner, Charles; Löwner, Karel (real name)
BRIEF DESCRIPTION Czech-American mathematician
DATE OF BIRTH May 29, 1893
PLACE OF BIRTH Lana
DATE OF DEATH January 8, 1968
Place of death Stanford , California