Vladimir Andreyevich Markov (1871-1897)

  • Alternative spelling: Markoff

  • Markov, V. A., O funktsiyakh, naimeneye uklonyayushchikhsya ot nulya v dannom promezhutke [On functions which deviate least from zero in a given interval], 1892. This was a preprint/treatise from the Department of Applied Mathematics, Imperial St.-Petersburg University. It was translated into German, with a short foreword by Bernstein, and appeared as: Über Polynome, die in einem gegebenen Intervalle möglichst wenig von Null abweichen Math. Ann. 77 (1916), 213-258. The paper contains the proof of the Markov inequality for higher derivatives of algebraic polynomials. The appendix of V. A. Gusev in the book of E. V. Voronovskaja titled "The Functional Method and its Applications", Vol. 28 of Translations of Mathematical Monographs of the AMS, 1970, reproduces the final (and most essential) part of Markov's proof almost identically (even the letters in formulae are the same). Vladimir Andreyevich Markov was a younger half-brother of Andrey Andreyevich Markov. This paper was published while he was a 21 year old student at the St.-Petersburg University. He died at the age of 25 (of tuberculosis).