# Nikolai Kapitonovich Nikolski

Nikolai Kapitonovich Nikolski (Николай Капитонович Никольский, sometimes transliterated as Nikolskii, born 16 November 1940) is a Russian mathematician, specializing in real and complex analysis and functional analysis.
Nikolski received in 1966 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). In 1973 he received his Doctor of Sciences degree (habilitation). He was an academician at the Steklov Institute of Mathematics in Leningrad and taught at Leningrad State University. In the 1990s he became a professor at the University of Bordeaux.
Nikolski's research deals with operator theory, harmonic analysis, and complex analysis.
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 2012 he was elected a Fellow of the American Mathematical Society.
His doctoral students include Nikolai Makarov, Sergei Treil, and Alexander Volberg.
Nikolski was one of the Leningrad mathematicians who in 1984 verified the correctness of the proof of the Bieberbach conjecture by Louis de Branges.

## Selected publications
### Articles

* Nikolski, Nikolai (1995). "Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann ζ-function". Annales de l'Institut Fourier. 45 (1): 143–159. doi:10.5802/aif.1451.
* Nikolski, Nikolai (1999). "In search of the invisible spectrum". Ann. Inst. Fourier (Grenoble). 49 (6): 1925–1998. doi:10.5802/aif.1743.
* with V. I. Vasyunin: Nikolski, Nikolai; Vasyunin, Vasily (2012). "Invertibility threshold for H$^∞$ trace algebras, and effective matrix inversions". St. Petersburg Math. J. 23: 57–73. arXiv:1010.6090. doi:10.1090/S1061-0022-2011-01186-0. S2CID 53397504; Original publication: Algebra i Analiz, tom 23 (2011), comer 1{{cite journal}}: CS1 maint: postscript (link)
* Nikolski, Nikolai (2012). "In a shadow of the RH: Cyclic vectors of Hardy spaces on the Hilbert multidisc". Annales de l'Institut Fourier. 62 (5): 1601–1626. doi:10.5802/aif.2731.
* Nikolski, N. (2014). "Sublinear dimension growth in the Kreiss Matrix Theorem". St. Petersburg Math. J. 25 (3): 361–396. doi:10.1090/S1061-0022-2014-01295-2; Original publication: Algebra i Analiz, tom 25 (2013), comer 3{{cite journal}}: CS1 maint: postscript (link)
* Nikolski, N. (2017). "Numerically detectable hidden spectrum of certain integration operators". St. Petersburg Math. J. 28 (6): 773–782. doi:10.1090/spmj/1472; Original publication: Algebra i Analiz, tom 28 (2016), comer 6{{cite journal}}: CS1 maint: postscript (link)

### 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
* 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