Mark Krein
Mark Grigoryevich Krein (Russian Марк Григорьевич Крейн; * 3 Apriljul / 16 April 1907greg in Kiev, .. † 17 October 1989 in Odessa) was a Soviet mathematician. His main area of work was the functional analysis, in particular, the operator theory and the theory of differential equations.
Life
Krein, who came from a family of Jewish timber merchant, showed early talent in mathematics and attended the age of 14 courses at the University of Odessa. In 1926 he was accepted despite the lack of previous university education of Nikolai Grigoryevich Chebotaryov for doctoral studies. In 1929 he received his PhD (Russian doctoral degrees, corresponding to Habilitation ) in Odessa and from then on remained at the university ( his doctor father Tschebotarjew had gone to Kazan in 1928 ). In Odessa, he established an important school of functional analysis. To her included, among other things, AP Artyomenko ( who was one of his most gifted student but was disappeared after the war ), David Milman, Witold Lvovitch Schmulian, Moshe Livsic, Mark A. Rutman and Vladimir A. Potapov and his colleague Boris Yakovlevich Levin in Odessa. During the German occupation of the Crimea from 1941 to 1944, he was evacuated to the University and was in Kuibyshev Aviation Institute. Although he came back to Odessa in 1944, but was soon released because of Jewish nationalism ( to Israel Gohberg probably because he had too many Jewish students in the 1930s ). Held at the University, he was Professor of Mechanics at the Institute of Marine Engineers in Odessa and was also part-time at the Mathematical Institute of the Ukrainian Academy of Sciences in Kiev, where he was but was released in 1952, officially because he did not live in Kiev. From 1954 he was professor at the Institute of Mechanics Civil Engineering in Odessa. Various attempts of mathematicians failed to bring it back to the University of Odessa. But Krein built again on a very active research group, which partially met in his private home as well as the Scientific Club of Odessa. Travel abroad was forbidden Krein.
Krein built in Odessa in the 1930s, a center for functional analysis to. He worked among others with Banach spaces, the problem of moments ( originally a from probability theory problem to reconstruct extent of their integrals ) integral equations and spectral theory of linear operators. With Naum Ilyich Achijeser he worked around 1937 also extremal differentiable periodic functions, an area on the Andrei Kolmogorov was previously pioneer. Later he studied with harmonic analysis, duality sets and operator algebras in representation theory. He wrote over 270 works and several monographs. Associated with his name, the terms Tannaka - Krein duality are ( additionally named after Tadao Tannaka ), Krein spaces and the Krein - Milman.
He became an honorary member of the American Academy of Arts and Sciences and in 1979 a foreign member of the National Academy of Sciences in 1968. In 1982 he was awarded the Wolf Prize, along with Hassler Whitney. In 1966 he gave a plenary lecture at the International Congress of Mathematicians in Moscow ( Analytic problems and results in the theory of linear operators in Hilbert space).
Among his doctoral students were David Milman, Witold Schmulian, Mark Aleksandrovich Krasnosel'skii, Mark Neumark, Israel Gohberg.
His younger brother Selim Grigoryevich Krein was also a mathematician and dealt with functional analysis.