Anatoli Georgievich Vitushkin

Anatoli Georgijewitsch Wituschkin (Russian Анатолий Георгиевич Витушкин, English transcription Anatoly Georgievich Vitushkin, . Born June 25, 1931 in Moscow, † May 9, 2004 ) was a Russian mathematician, who dealt with Analysis.

Wituschkin was a student of Andrei Kolmogorov at Moscow State University, where he graduated in 1954. In 1958 he received his doctorate in Kolmogorov (Estimation of the complexity of a tabulation problem). Since 1964 he worked at the Steklov Institute in Moscow and taught at the Moscow State University (Faculty of Mathematics and Mechanics ).

Wituschkin dealt with real and complex analysis and approximation theory. An assumption by him for subadditivity of analytic capacity (a term of Lars Ahlfors, whose fertility for the approximation theory Wituschkin detected) was proved by Xavier Tolsa 2003. Another conjecture of Wituschkin proved Guy David in 1998.

He made important contributions to the 13th Hilbert problem through his study of approximation of continuous functions of several variables by those with fewer variables ( a problem also on the Kolmogorov and his student Vladimir Arnold worked ). He also dealt with the complexity of algorithms for computing functions and their approximation.

Further work will address the complex geometry (real hypersurfaces in complex spaces of higher dimension and their behavior under holomorphic maps ).

In 1974 he gave a plenary lecture at the ICM in Vancouver (Coding of signal with finite spectrum and sound recording problems ) and in 1966 he was invited speaker at the ICM in Moscow (On the way to represent a function by superposition of functions of small number of variables ).