Edgar Krahn

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Edgar Krahn. Photo from the interwar period.

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

Life

Krahn's parents were of Estonian -German Baltic descent. He graduated from high school in Dorpat ( Tartu ) in 1912 and studied mathematics and physics at the University of Dorpat with the teaching examination in 1917.

Then he was a teacher in Dorpat and Reval ( Tallinn ). From the winter semester of 1922 he studied at the University of Göttingen , where he received his doctorate under Richard Courant in 1926 ( on minimal properties of the sphere in three and more dimensions ). After Hermann Jaakson (1891–1964), Krahn was the second Estonian to receive a doctorate in mathematics.

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

mathematics

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

In 1925 he proved a lower bound for the lowest eigenvalue of the Laplace operator (with Dirichlet boundary condition ) in a restricted area of ​​the and showed that the lower limit is assumed exactly for the circle or spheres. This was suspected in the two-dimensional case of John William Strutt, 3rd Baron Rayleigh , (Theory of Sound, Volume 1, § 210) and Courant had already achieved initial results. Georg Faber independently proved the two-dimensional case , Krahn also proved the n-dimensional case. The inequality is named after Rayleigh, Faber and Krahn.

Whereby the volume of the n-dimensional unit ball, V is the volume of the considered area, and the first positive zero of the Bessel function of the order .

The inequality assumed by Rayleigh results especially for two dimensions n = 2:

With the area A of the membrane.

In 1983 his widow Dorothee Krahn donated an Edgar Krahn Fellowship to the University of Maryland .

literature

  • Ulo Lumiste, Jaak Peetre (editor): Edgar Krahn 1894-1961. A centenary volume. IOS Press, Amsterdam 1994 (in collaboration with the Estonian Mathematical Society).

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. First in an essay on the probability of the four-color presumption being true , The probability of the correctness of the four-color theorem , Acta Comment. Univ. Dorpatensis, A 22, 1932, No. 2, pp. 1-7.
  3. Krahn On a minimal property of the circle formulated by Rayleigh , Mathematische Annalen, Volume 94, 1925, pp. 97-100, On minimal properties of the sphere in three and more dimensions , Acta et Commentationes Universitatis Dorpatensis, A, Volume 9, 1926, p. 1-44
  4. ^ "Proof of the theorem that of all homogeneous membranes of a given circumference and given tension, the circular one has the lowest keynote", Mathematische Zeitschrift, Volume 1, 1918, pp. 321–328
  5. Faber "Proof that among all homogeneous membranes of the same area and the same tension the circular one gives the lowest keynote", Sitzungsber. Bayer. Akad. Wiss. Munich, Math.-Phys. Class 1923, pp. 169-172
  6. Rayleigh-Faber-Krahn Inequality, Encyclopedia of Mathematics
  7. ^ Krahn Fellowship ( Memento from May 13, 2013 in the Internet Archive )