Vladimir Marchenko

Vladimir Alexandrovich Marchenko (Russian: Влади́мир Алекса́ндрович Ма́рченко, Ukrainian: Володи́мир Олекса́ндрович Ма́рченко; born July 7, 1922) is a Soviet and Ukrainian mathematician who specializes in mathematical physics.[1]

For the Russian gymnast, see Vladimir Marchenko (gymnast).

Biography

Vladimir Marchenko was born in Kharkiv in 1922. He defended his PhD thesis in 1948 under the supervision of Naum Landkof, and in 1951 he defended his DSc thesis. He worked in Kharkiv University until 1961. For 4 decades, he headed the Mathematical Physics Department at the B Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine.

He was awarded the Lenin Prize in 1962, the N. N. Krylov Prize in 1980, the State Prize of the Ukrainian SSR in 1989, and the N. N. Bogolyubov prize in 1996. Since 1969 he is a member of the National Academy of Sciences of Ukraine, since 1987 of the Russian Academy of Sciences and since 2001 of the Royal Norwegian Society of Sciences and Letters.[1]

Work

Differential operators

Marchenko made fundamental contributions to the analysis of the Sturm–Liouville operators. He introduced one of the approaches to the inverse scattering problem for Sturm–Liouville operators, and derived what is now called the Marchenko equation.

Random matrices

Together with Leonid Pastur, Vladimir Marchenko discovered the Marchenko–Pastur law in random matrix theory.

Homogenization

Together with E. Ya. Khruslov, Marchenko authored one of the first mathematical books on homogenization.[2]

Notes
  1. Berezanskiĭ, Yu. M.; Zakharov, V. E.; Mitropolʹskiĭ, Yu. A.; Ostrovskii, I. V.; Pastur, L. A.; Pogorelov, A. V.; Rofe-Beketov, F. S.; Skrypnik, I. V.; Khruslov, E. Ya. (2003), "Vladimir Aleksandrovich Marchenko (on the occasion of his eightieth birthday)", Russian Math. Surveys, 58 (4): 813–816, doi:10.1070/rm2003v058n04abeh000660, MR 2042920
  2. Marčenko & Khruslov (1974)

Selected publications
  • Marčenko, V. A.; Khruslov, E. Ya. (1974), Boundary value problems in domains with a fine-grained boundary (in Russian), Kiev: Naukova Dumka, MR 0601059. The second edition was translated into English: Marchenko, V. A.; Khruslov, E. Ya. (2006), Homogenization of partial differential equations, Progress in Mathematical Physics, 46, Boston, MA: Birkhäuser Boston, Inc., ISBN 978-0-8176-4351-5, MR 2182441
  • Marchenko, V. A. (2011), Sturm-Liouville operators and applications (2 ed.), Providence: American Mathematical Society, doi:10.1090/chel/373, ISBN 978-0-8218-5316-0, MR 2798059.
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