mathematics

Nikolai Kapitonovich Nikolski

Nikolai Kapitonovich Nikolski is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Nikolai Kapitonovich Nikolski rather than just read about it. In short: 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. 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…

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Reference excerpt

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. 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). 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, 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) include Alexander Borichev, Nikolai Makarov, Sergei Treil, Vasily Vasyunin, 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.

Selected publications

Articles Nikolski, Nikolai (1999). "In search of the invisible spectrum". Ann. Inst. Fourier (Grenoble). 49 (6): 1925–1998. doi:10.5802/aif.1743. Nikolski, Nikolai (1999). "Remarks concerning completeness of translates in function spaces". J. Approx. Theory. 98 (2): 303–315. doi:10.1006/jath.1999.3365. Nikolski, Nikolai; Gorkin, P.; Mortini, R. (2008). "Norm controlled inversions and a corona theorem for H∞-quotient algebras". Journal of Functional Analysis. 255 (4): 854–876. doi:10.1016/j.jfa.2008.05.011. 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, Nikolai; Verbitsky, I. (2017). "Fourier multipliers for weighted L² spaces with Lévy–Khinchin–Schoenberg weights". J. Reine Angew. Math. 731: 159–201. arXiv:1404.4380. doi:10.1515/crelle-2014-0123. Nikolski, Nikolai (2022). "Three dimensions of metric-measure spaces, Sobolev embeddings and optimal sign transport". Algebra i Analiz. 34 (2): 118–151.

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). (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). (III) Operators, Functions, and Systems. An easy reading, Vol. 1 and Vol. 2, Mathematical Surveys and Monographs, American Mathematical Society, Providence, 2002; . (IV) Treatise on the Shift Operator, Grundlehren der mathematischen Wissenschaften 273, Springer Verlag 1986 (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 Editor, an excerpt ”Zapiski Nauchnyh Seminarov LOMI (Leningrad Branch of the Steclov Mathematical Institute)”: - volumes 19 (1970), 22 (1971), 30 (1972), 39 (1974), 47 (1974), 56 (1976), 65 (1976), 73 (1977), 81 (1978; with V.P.Havin), etc - more than 25 issues, up to vol. 255 (1998).

”Trudy Math. Inst. Steklova”, Moscow, (Russian); English transl.: ”Proc. Steklov Math. Inst.”, AMS, Providence: - vol.130 ”Spectral Theory of Functions and Operators”, 1978, 223 pp; English transl.: Proc. Steklov Math. Inst., 130 (1979), AMS, Providence. - vol.155 ”Spectral Theory of Functions and Operators. II”, 1981, 187 pp; English transl.: Proc. Steklov Math. Inst., 155(1982), AMS, Providence.

”Encyclopaedia of Mathematical Sciences”, Springer-Verlag; co-editor, volumes 15,19,25,42,72,85; 1990 - 1996. ”Operator Theory: Advances and Applications”, a Birkhäuser series: - ”Toeplitz operators and spectral function theory. Essays from the Leningrad Seminar on Operator Theory”, vol.42 (1989), 425 pp., Zbl 0677.00024. - (with V.P.Havin) ”Complex Analysis, Operators, and Related Topics. The S.A.Vinogradov memo- rial volume”, vol.113 (2000), 408 pp., Zbl 0934.00031. - (with A.Borichev) ”Systems, Approximation, Singular Integral Operators, and Related Topics”, IWOTA 2000 Proceedings; vol.129 (2001), 527 pp., Zbl 0972.00051. - (with A.Baranov and S.Kisliakov) ”50 Years with Hardy Spaces. A tribute to Victor Havin”, vol.261 (2018), 484 pp., Zbl 06848809.

”Lecture Notes in Mathematics”, Springer-Verlag: - (with V.P.Havin) ”Complex Analysis and Spectral Theory. Seminar, Leningrad 1979/1980”, vol.864 (1981), 480 pp. - (with V.P.Havin) ”Linear and Complex Analysis Problem Book 3. 341 research problems”, vol. I: 1573 (1994), 488 pp., Zbl 0893.30036; Vol.II: 1574 (1994), 507 pp., Zbl 0893.30037.

(with E.Charpentier) ”Lécons de Mathématiques d’Aujourd’hui”, Vols. 1(2000), 2(2003), and 3(2007), Cassini, Paris. (with E.Charpentier and A.Lesne) ”L’héritage de Kolmogorov en mathématiques”, (French) Zbl 1137.00330, Collection Echelles. Paris: Belin (ISBN 2-7011-3669-5). 303 pp. (2004). Engl. transl.: ”Kolmogorov’s heritage in mathematics”, Zbl 1136.00010, Berlin: Springer (ISBN 978-3-540-36349-1/hbk). viii, 317 pp. (2007). (See Ref. 3 below).

References

External links mathnet.ru Nicolas Nikolski, fiche personnelle, Université de Bordeaux

Illustrations

Worked examples

Example 1 — a first encounter with Nikolai Kapitonovich Nikolski

Start with the simplest possible case. Write down what Nikolai Kapitonovich Nikolski claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Nikolai Kapitonovich Nikolski before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Nikolai Kapitonovich Nikolski ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Nikolai Kapitonovich Nikolski

In research: Nikolai Kapitonovich Nikolski appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Nikolai Kapitonovich Nikolski in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Nikolai Kapitonovich Nikolski is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1940 births, 20th-century Russian mathematicians, 21st-century Russian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Nikolai Kapitonovich Nikolski outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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