Dmitrii Menshov

Dmitri Jewgenjewitsch Menshov (Russian: Дмитрий Евгеньевич Меньшов, English transcription Dmitrii Evgenevich Menshov; * 6 Apriljul / April 18 1892greg in Moscow, .. † 25 November 1988) was a Russian mathematician who mainly dealt with real analysis.

Menshov was the son of a doctor and studied from 1912 at the Moscow State University with Dmitri Egorov and Nikolai Nikolaevich Luzin. Even before graduating, he published his first work, which triggered an upside of Lusin problem ( ratio of the Borel integral of the Denjoy integral, Menshov showed that the Borel integral a special case of Denjoy integral is ). In 1916 he received his diploma with a thesis on Riemann's theory of Fourier series shear. In 1918 he received his doctorate and became a professor in Nizhny Novgorod and a little later in Ivanovo at the Pedagogical Institute and also taught at the Polytechnic Institute. From 1921 he taught at the Moscow State University and other universities in Moscow. He had not formally habilitation (Russian doctoral degree ), but received in 1935 the Russian doctoral degree for his published work and became a professor at Moscow State University. In 1927, he visited with a Rockefeller scholarship to Paris, where he took part in the seminar, among other things by Jacques Hadamard. In 1941 he was awarded as the successor of Ivan Ivanovich Priwalow the Chair of function theory, starting in 1943 combined with the Chair of Functional Analysis. 1934 to 1941 and from 1947 he was also at the Steklov Institute.

In 1916 he proved by giving an example that a Fourier series that converges to zero to points from a set of measure zero, can not have vanishing Fourier coefficients. Before Georg Cantor had proved that for Fourier series that converge to a countable set of points to zero, the coefficients disappear. In addition to real analysis, he was also involved in complex analysis.

In 1951 he was awarded the Soviet State Prize. In 1953 he became a corresponding member of the Soviet Academy of Sciences. In 1958 he was invited speaker on the ICM in Edinburgh (On the convergence of trigonometric series).

Writings

• Les conditions de monogénéité, Paris, Hermann, 1936
• Limits of indeterminacy in measure of T -means of subseries of a trigonometric series, American Mathematical Society, 1968, 1981
• Selected Works, Moscow 1997 ( Russian)