Nikolai Kapitonovich Nikolski

Nikolai Kapitonovich Nikolski (Николай Капитонович Никольский, sometimes transliterated as Nikolskii, born 16 November 1940)[1] is a Russian mathematician, specializing in real and complex analysis and functional analysis.

In 1966, Nikolski earned his Candidate of Sciences degree (PhD) from the Leningrad State University under Viktor Khavin with thesis Invariant subspaces of certain compact operators (title translated from Russian).[2] In 1973 he received his Doctor of Sciences degree (habilitation) published as monograph (VI) below. He was a Laboratory director (of Math Analysis) at the Steklov Institute of Mathematics in Leningrad and Professor of Department of Mathematics at Leningrad State University. In 1991 he became a professor at the University of Bordeaux.

Nikolski's research deals with operator theory, harmonic analysis, and complex analysis. He has published more than 100 papers and six research monographs.

He was an Invited Speaker with talk What problems do spectral theory and functional analysis solve for each other? at the ICM in 1978 in Helsinki. In 2010, he was awarded the Ampère Prize of the French Academy of Sciences,[3] and in 2012 he was elected a Fellow of the American Mathematical Society, as well as for several temporary positions as Fellow of the Advanced Study Institute at Indiana University (Bloomington, 1988), Distinguished Visiting Scholar, Ben-Gurion University (Israel, 1993), MSRI Research grant (Berkeley, 1995), Marie Curie Action Senior Fellow, TODEQ Project, 2008, Taussky-Todd Distinguished Professor, Caltech (Pasadena, 2015).

His doctoral students (total 26[2]) include Alexander Borichev, Nikolai Makarov, Sergei Treil, Vasily Vasyunin and Alexander Volberg.

Among his notable contributions, Nikolski was one of the Leningrad mathematicians who in 1984 verified the correctness of the proof of the Bieberbach conjecture by Louis de Branges.[4]

Selected publications

Articles

Research Monographs

(I) Toeplitz matrices and operators, Cambridge Studies in Advanced Mathematics, 182, Cambridge University Press, Cambridge, 2020 (French original: Matrices et opérateurs de Toeplitz, C&M, Paris, 2017); Ref. 10.

(II) Hardy Spaces, Cambridge University Press, Cambridge Studies in Advanced Mathematics, 179, Cambridge, 2019 (French original: Éléments d’analyse avancée. Espaces de Hardy, Belin, Paris, 2012); Ref. 7.

(III) Operators, Functions, and Systems. An easy reading, Vol. 1 and Vol. 2, Mathematical Surveys and Monographs, American Mathematical Society, Providence, 2002; Ref. 11.

(IV) Treatise on the Shift Operator, Springer, Heidelberg, 1986; second printing 2012; Ref. 4.

(V) Lectures on the Shift Operator (Russian: «Лекции об операторе сдвига»), Nauka, Moscow, 1980.

(VI) Selected problems of weighted approximation and spectral analysis, American Mathematical Society, Providence, 1976, Zbl 0342.41028 (Russian original: «Избранные задачи весовой аппроксимации и спектрального анализа», Trudy Mat. Inst. Steklova, vol. 120, Moscow, 1974, Zbl 0342.41027).

Books

  • as editor: Investigations in linear operators and function theory, New York: Consultants Bureau 1972
  • as editor: Spectral theory of functions and operators , 2 vols., American Mathematical Society 1980
  • as editor with Viktor Petrovich Khavin and Sergei V. Khrushchev: Linear and complex analysis problem book: 199 research problems, Springer Verlag 1984
  • with V. P. Khavin: Linear and complex analysis problem book 3, 2 vols., Springer Verlag 1994
  • as editor: Toeplitz operators and spectral function theory: essays from the Leningrad Seminar on Operator Theory, Birkhäuser 1989
  • as editor with Éric Charpentier and Annick Lesne: Kolmogorov's Heritage in Mathematics. Springer Verlag 2007.[5]
  • as editor: Functional analysis I: linear functional analysis, Springer Verlag 1992
  • as editor with V. P. Khavin: Complex analysis, operators, and related topics : the S.A. Vinogradov memorial volume, Birkhäuser 2000
  • Treatise on the shift operator. Spectral function theory, Grundlehren der mathematischen Wissenschaften 273, Springer Verlag 1986[6]

References

  1. ^ date of birth from Viaf.
  2. ^ a b Nikolai Kapitonovich Nikolskii at the Mathematics Genealogy Project.
  3. ^ https://www.canalacademies.com/emissions/sous-la-coupole/academie-des-sciences/seance-solennelle-de-rentree-de-lacademie-des-sciences-2010-1-2.
  4. ^ Karl Sabbagh, Dr. Riemann's zeros, pp. 279, Atlantic Publisher, ISBN 1-84354-101-7, 2003. (Extended version: The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics, Eds.: Farrar, Straus, and Giroux, 2003, ISBN 0374250073, 9780374250072, 340 pp).
  5. ^ Marchisotto, Elena Anne (5 December 2007). "Review of Kolmogorov's Heritage in Mathematics by Charpentier, Lesne, & Nikolski, editors". MAA Reviews, Mathematical Association of America.
  6. ^ Sarason, Donald (1987). "Review of Treatise on the Shift Operator. Spectral Function Theory by N. K. Nikol′skiĭ". Bull. Amer. Math. Soc. (N.S.). 16: 297–298. doi:10.1090/S0273-0979-1987-15522-4.
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