Edgar Krahn

Edgar Krahn (born 19 Septemberjul / October 1 1894greg in Sootaga, Governorate of Livonia, today the village of Laish, Republic of Estonia, .. † March 6, 1961 in Rockville, Maryland) was an Estonian mathematician.

Life

Krahns parents were Estonian- deutschbaltischer descent. He made in 1912 in Dorpat (Tartu ) graduated from high school and studied at the University of Dorpat with the Magisterium exam 1917 in mathematics and physics.

After that, he was a teacher in Dorpat and Reval (Tallinn ). Starting in the winter semester 1922 he studied at the University of Göttingen, where he received his doctorate in 1926 with Richard Courant (over the minimum properties of the sphere in three or more dimensions). Krahn was after Jaakson Hermann (1891-1964), the second Este, who holds a doctorate in mathematics.

In 1928 he qualified as a professor in Dorpat, where he was professor. In the 1940s he was at the Aerodynamic Research Institute in Göttingen, where he (as well as later in the UK and the USA ) dealt with fluid mechanics. In the early 1950s he worked for the Admiralty Research Laboratory in the UK and then for the Naval Ordnance Laboratory in White Oak, Maryland in the United States.

Mathematics

Edgar Krahn dealt with differential equations, differential geometry, insurance mathematics (especially for building societies ), probability theory, gas dynamics and elasticity theory.

He proved in 1925 a lower bound for the lowest eigenvalue of the Laplacian ( with Dirichlet boundary condition) in a limited area of ​​and showed that the lower limit is assumed accurate for the circle or balls. That was in the two-dimensional case of Lord Rayleigh ( Theory of Sound, Volume 1, § 210) was suspected, and the first results achieved already Courant. The two-dimensional case proved independently Georg Faber, Krahn also proved the n- dimensional case. The inequality is named after Rayleigh, Faber and Krahn.

Wherein the volume of the n-dimensional unit ball, V the volume of the observed region, and the first positive zero of the Bessel function of order.

Especially for two dimensions n = 2 gives the assumed Rayleigh inequality:

With the area A of the membrane.

In 1983, his widow Dorothee Krahn an Edgar Krahn Fellowship at the University of Maryland.