Nikolʹskiĭ, N. K. (Nikolaĭ Kapitonovich)
Overview
Works:  127 works in 539 publications in 4 languages and 7,145 library holdings 

Genres:  History Festschriften Conference papers and proceedings 
Roles:  Author, Editor, Publishing director, Thesis advisor, Other, ed, Honoree, Opponent 
Publication Timeline
.
Most widely held works by
N. K Nikolʹskiĭ
Treatise on the shift operator : spectral function theory by
N. K Nikolʹskiĭ(
Book
)
32 editions published between 1980 and 2012 in 3 languages and held by 464 WorldCat member libraries worldwide
This book is an elementary introduction to nonclassical spectral theory. Mter the basic definitions and a reduction to the study of the functional model the discussion will be centered around the simplest variant of such a model which, formally speaking, comprises only the class of contraction operators with a one dimensional rank of nonunitarity (rank(I  T*T) = rank(I  TT*) = 1). The main emphasis is on the technical side of the subject, the book being mostly devoted to a development of the analytical machinery of spectral theory rather than to this discipline itself. The functional model of Sz.Nagy and Foia{sect} re duces the study of general operators to an investigation of the . compression T=PSIK of the shift operator S, Sf = zf, onto coinvariant subspaces (i. e. subspaces in variant with respect to the adjoint shift S*). In the main body of the book (the "Lectures" in the proper meaning of the word) this operator acts on the Hardy space H2 and is itself a part of the operator of multiplication by the independent variable in the space L2 (in the case at hand L2 means L2(lf), If being the unit circle), this operator again being fundamental for classical spectral theory
32 editions published between 1980 and 2012 in 3 languages and held by 464 WorldCat member libraries worldwide
This book is an elementary introduction to nonclassical spectral theory. Mter the basic definitions and a reduction to the study of the functional model the discussion will be centered around the simplest variant of such a model which, formally speaking, comprises only the class of contraction operators with a one dimensional rank of nonunitarity (rank(I  T*T) = rank(I  TT*) = 1). The main emphasis is on the technical side of the subject, the book being mostly devoted to a development of the analytical machinery of spectral theory rather than to this discipline itself. The functional model of Sz.Nagy and Foia{sect} re duces the study of general operators to an investigation of the . compression T=PSIK of the shift operator S, Sf = zf, onto coinvariant subspaces (i. e. subspaces in variant with respect to the adjoint shift S*). In the main body of the book (the "Lectures" in the proper meaning of the word) this operator acts on the Hardy space H2 and is itself a part of the operator of multiplication by the independent variable in the space L2 (in the case at hand L2 means L2(lf), If being the unit circle), this operator again being fundamental for classical spectral theory
Linear and complex analysis problem book : 199 research problems by
Viktor Petrovich Khavin(
Book
)
17 editions published in 1984 in 3 languages and held by 374 WorldCat member libraries worldwide
17 editions published in 1984 in 3 languages and held by 374 WorldCat member libraries worldwide
Commutative harmonic analysis I : general survey, classical aspects by
Viktor Petrovich Khavin(
Book
)
32 editions published between 1987 and 2011 in English and Undetermined and held by 366 WorldCat member libraries worldwide
This is the first volume in the subseries Commutative Harmonic Analysis of the EMS. It is intended for anyone who wants to get acquainted with the discipline. The first article is a large introduction, also serving as a guide to the rest of the volume. Starting from Fourier analysis of periodic function, then going through the Fourier transform and distributions, the exposition leads the reader to the group theoretic point of view. Numer rous examples illustrate the connections to differential and integral equations, approximation theory, number theory, probability theory and physics. The article also contains a brief historical essay on the development of Fourier analysis. The second article focuses on some of the classical problems of Fourier series; it's a "miniZygmund" for the beginner. In particular, the convergence and summability of Fourier series, translation invariant operators and theorems on Fourier coefficients are given special attention. The third article is the most modern of the three, concentrating on the theory of singular integral operators. The simplest such operator, the Hilbert transform, is covered in detail. There is also a thorough introduction to CalderonZygmund theory
32 editions published between 1987 and 2011 in English and Undetermined and held by 366 WorldCat member libraries worldwide
This is the first volume in the subseries Commutative Harmonic Analysis of the EMS. It is intended for anyone who wants to get acquainted with the discipline. The first article is a large introduction, also serving as a guide to the rest of the volume. Starting from Fourier analysis of periodic function, then going through the Fourier transform and distributions, the exposition leads the reader to the group theoretic point of view. Numer rous examples illustrate the connections to differential and integral equations, approximation theory, number theory, probability theory and physics. The article also contains a brief historical essay on the development of Fourier analysis. The second article focuses on some of the classical problems of Fourier series; it's a "miniZygmund" for the beginner. In particular, the convergence and summability of Fourier series, translation invariant operators and theorems on Fourier coefficients are given special attention. The third article is the most modern of the three, concentrating on the theory of singular integral operators. The simplest such operator, the Hilbert transform, is covered in detail. There is also a thorough introduction to CalderonZygmund theory
Linear and complex analysis problem book 3 by
Viktor Petrovich Khavin(
Book
)
23 editions published between 1994 and 2008 in English and held by 322 WorldCat member libraries worldwide
Presents a collection of unsolved problems of modern analysis designed as informally written miniarticles, each containing not only a statement of a problem but also historical and methodological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references
23 editions published between 1994 and 2008 in English and held by 322 WorldCat member libraries worldwide
Presents a collection of unsolved problems of modern analysis designed as informally written miniarticles, each containing not only a statement of a problem but also historical and methodological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references
Investigations in linear operators and function theory by
N. K Nikolʹskiĭ(
Book
)
7 editions published in 1972 in English and held by 197 WorldCat member libraries worldwide
7 editions published in 1972 in English and held by 197 WorldCat member libraries worldwide
Selected problems of weighted approximation and spectral analysis by
N. K Nikolʹskiĭ(
Book
)
8 editions published in 1976 in English and held by 196 WorldCat member libraries worldwide
8 editions published in 1976 in English and held by 196 WorldCat member libraries worldwide
Toeplitz operators and spectral function theory : essays from the Leningrad Seminar on Operator Theory by
N. K Nikolʹskiĭ(
Book
)
12 editions published in 1989 in English and held by 183 WorldCat member libraries worldwide
The volume contains selected papers of the Spectral Function Theory seminar, Leningrad Branch of Steklov Mathematical Institute. The papers are mostly devoted to the theory of Toeplitz and model operators. These subjects are considered here from various points of view. Several papers concern the relationships of Toeplitz operators to weighted polynomial approximation. Namely, two papers by B. Solomyak and A. Volberg intensively treat the problem of spectra! multiplicity f~r analytic Toeplitz operators (which are, in fact, multiplication operators) and my paper can serve as an introduction to the problem. This theme of multiplicities is continued in a paper by V. Vasyunin where the multiplicity of the spectrum is computed for Hilbert space contractions with finite defect indices. V. Peller's paper deals with a perturbation theory problem for Toeplitz operators. In a paper by D. Yakubovich a new similarity model for a class of Toeplitz operators is constructed. S. Treil' presents a survey of a part of spectral function theory for vector valued function (SzegoKolmogorov extreme prob!ems for operator weights, bases of vector rational functions, estimations of Hilbert transform with respect to operator weights, the operator corona problem). As a concluding remark I dare only note that the whole collection convinces us once more without a doubt of the fruitfullness of the natural union of operator theory and complex analysis (if at all the union of these fields is at all different from their intersection)
12 editions published in 1989 in English and held by 183 WorldCat member libraries worldwide
The volume contains selected papers of the Spectral Function Theory seminar, Leningrad Branch of Steklov Mathematical Institute. The papers are mostly devoted to the theory of Toeplitz and model operators. These subjects are considered here from various points of view. Several papers concern the relationships of Toeplitz operators to weighted polynomial approximation. Namely, two papers by B. Solomyak and A. Volberg intensively treat the problem of spectra! multiplicity f~r analytic Toeplitz operators (which are, in fact, multiplication operators) and my paper can serve as an introduction to the problem. This theme of multiplicities is continued in a paper by V. Vasyunin where the multiplicity of the spectrum is computed for Hilbert space contractions with finite defect indices. V. Peller's paper deals with a perturbation theory problem for Toeplitz operators. In a paper by D. Yakubovich a new similarity model for a class of Toeplitz operators is constructed. S. Treil' presents a survey of a part of spectral function theory for vector valued function (SzegoKolmogorov extreme prob!ems for operator weights, bases of vector rational functions, estimations of Hilbert transform with respect to operator weights, the operator corona problem). As a concluding remark I dare only note that the whole collection convinces us once more without a doubt of the fruitfullness of the natural union of operator theory and complex analysis (if at all the union of these fields is at all different from their intersection)
Complex analysis, operators, and related topics : the S.A. Vinogradov memorial volume(
Book
)
11 editions published between 1991 and 2000 in English and held by 173 WorldCat member libraries worldwide
This volume is devoted to some topical problems and various applications of operator theory and its interplay with modern complex analysis. It consists of 30 carefully selected surveys and research papers. The main subjects of the volume include: free interpolation by analytic functions in its development from the pathbreaking works by L. Carleson up to the most recent achievements and in its connections with the theory of singular integral operators and Carlesontype embedding theorems, moment problems etc. SzkefalviNagyFoias model spaces studied from the point of view of holomorphic spaces holomorphic spaces (Hardy, Bergman, Hlder, and Sobolev spaces) analytic functions smooth up to the boundary with their subtle properties related to the NevanlinnaSmirnov factorization, division and multiplication, and zero sets a new approach to weighted inequalities for singular integrals based on the Bellman function in optimization theory; the uncertainty principle in harmonic analysis and, in particular, a complete version of Turans lemma on trigonometric sums Hankel operators and stationary Gaussian processes Fourier multipliers, and spectral analysis of some differential operators. These themes are united by the "operator theoretic ideology" and systematic use of modern function theoretical techniques. The book is dedicated to the memory of S.A. Vinogradov. It contains a bibliographical note (with a lively portrait) of S.A. Vinogradov, a detailed survey of his mathematical achievements, and a complete list of publications, as well as the translations of two of Vinogradovs surveys whose Russian originals are now hardly accessible
11 editions published between 1991 and 2000 in English and held by 173 WorldCat member libraries worldwide
This volume is devoted to some topical problems and various applications of operator theory and its interplay with modern complex analysis. It consists of 30 carefully selected surveys and research papers. The main subjects of the volume include: free interpolation by analytic functions in its development from the pathbreaking works by L. Carleson up to the most recent achievements and in its connections with the theory of singular integral operators and Carlesontype embedding theorems, moment problems etc. SzkefalviNagyFoias model spaces studied from the point of view of holomorphic spaces holomorphic spaces (Hardy, Bergman, Hlder, and Sobolev spaces) analytic functions smooth up to the boundary with their subtle properties related to the NevanlinnaSmirnov factorization, division and multiplication, and zero sets a new approach to weighted inequalities for singular integrals based on the Bellman function in optimization theory; the uncertainty principle in harmonic analysis and, in particular, a complete version of Turans lemma on trigonometric sums Hankel operators and stationary Gaussian processes Fourier multipliers, and spectral analysis of some differential operators. These themes are united by the "operator theoretic ideology" and systematic use of modern function theoretical techniques. The book is dedicated to the memory of S.A. Vinogradov. It contains a bibliographical note (with a lively portrait) of S.A. Vinogradov, a detailed survey of his mathematical achievements, and a complete list of publications, as well as the translations of two of Vinogradovs surveys whose Russian originals are now hardly accessible
Kolmogorov's heritage in mathematics by
Éric Charpentier(
Book
)
14 editions published between 2007 and 2010 in English and Undetermined and held by 147 WorldCat member libraries worldwide
"A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject. Most mathematicians prove what they can, Kolmogorov was of those who prove what they want. For this book several world experts were asked to present one part of the mathematical heritage left to us by Kolmogorov."Publisher's website
14 editions published between 2007 and 2010 in English and Undetermined and held by 147 WorldCat member libraries worldwide
"A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject. Most mathematicians prove what they can, Kolmogorov was of those who prove what they want. For this book several world experts were asked to present one part of the mathematical heritage left to us by Kolmogorov."Publisher's website
Spectral theory of functions and operators(
Book
)
in English and held by 120 WorldCat member libraries worldwide
in English and held by 120 WorldCat member libraries worldwide
Systems, approximation, singular integral operators, and related topics : International Workshop on Operator Theory and Applications,
IWOTA 2000 by
Alexander A Borichev(
Book
)
8 editions published in 2001 in English and held by 101 WorldCat member libraries worldwide
This book is devoted to some topical problems and applications of operator theory and its interplay with modern complex analysis. It consists of 20 selected survey papers that represent updated (mainly plenary) addresses to the IWOTA 2000 conference held at Bordeaux from June 13 to 16, 2000. The main subjects of the volume include:  spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers;  multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations;  Hankel operators and forms;  operator algebras;  the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations;  approximation in holomorphic spaces. These subjects are unified by the common "operator theoretic approach" and the systematic use of modern function theory techniques
8 editions published in 2001 in English and held by 101 WorldCat member libraries worldwide
This book is devoted to some topical problems and applications of operator theory and its interplay with modern complex analysis. It consists of 20 selected survey papers that represent updated (mainly plenary) addresses to the IWOTA 2000 conference held at Bordeaux from June 13 to 16, 2000. The main subjects of the volume include:  spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers;  multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations;  Hankel operators and forms;  operator algebras;  the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations;  approximation in holomorphic spaces. These subjects are unified by the common "operator theoretic approach" and the systematic use of modern function theory techniques
Leçons de mathématiques d'aujourd'hui(
Book
)
7 editions published between 2003 and 2012 in French and held by 87 WorldCat member libraries worldwide
7 editions published between 2003 and 2012 in French and held by 87 WorldCat member libraries worldwide
Leçons de mathématiques d'aujourd'hui by
JeanPierre Kahane(
Book
)
6 editions published in 2000 in French and held by 84 WorldCat member libraries worldwide
6 editions published in 2000 in French and held by 84 WorldCat member libraries worldwide
L'héritage de Kolmogorov en mathématiques by
Éric Charpentier(
Book
)
7 editions published in 2004 in French and held by 82 WorldCat member libraries worldwide
A.N. Kolmogorov, dont on célèbre le centenaire de la naissance, fut peutêtre le plus grand mathématicien du XXe siècle. Il a eu des contributions importantes en probabilité, en théorie du chaos ou en complexité algorithmique. Propose un tour d'horizon de son oeuvre mathématique
7 editions published in 2004 in French and held by 82 WorldCat member libraries worldwide
A.N. Kolmogorov, dont on célèbre le centenaire de la naissance, fut peutêtre le plus grand mathématicien du XXe siècle. Il a eu des contributions importantes en probabilité, en théorie du chaos ou en complexité algorithmique. Propose un tour d'horizon de son oeuvre mathématique
Leçons de mathématiques d'aujourd'hui(
Book
)
1 edition published in 2003 in French and held by 82 WorldCat member libraries worldwide
1 edition published in 2003 in French and held by 82 WorldCat member libraries worldwide
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Related Identities
 Khavin, Viktor Petrovich Thesis advisor Author Editor
 Charpentier, Éric Other Publishing director Author Editor
 Lesne, Annick Publishing director Editor
 Khrushchev, S. V. Writer of accompanying material Editor
 Kolmogorov, A. N. (Andreĭ Nikolaevich) 19031987 Author
 Gonchar, A. A. (Andrei A.) Editor
 Matematicheskiĭ institut im. V.A. Steklova
 Vinogradov, S. A. (Stanislav Aleksandrovich) 19411997 Dedicatee
 Borichev, Alexander A. 1963 Author Editor
 Kahane, JeanPierre Other Author
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Associated Subjects
Analytic functions Approximation theory Differentiable dynamical systems Distribution (Probability theory) Fourier analysis Fourier series Functional analysis Functions Functions of complex variables Functions of several complex variables Global analysis (Mathematics) Harmonic analysis Harmonic functions Influence (Literary, artistic, etc.) Invariant subspaces Kolmogorov, A. N.(Andreĭ Nikolaevich), Kolmogorov complexity Linear operators Logic, Symbolic and mathematical Mathematical analysis Mathematics Operator theory Potential theory (Mathematics) Shift operators (Operator theory) Spectral theory (Mathematics) Toeplitz operators Topological groups Topology
Alternative Names
Nikolai Kapitonowitsch Nikolski mathématicien russe
Nikolai Kapitonowitsch Nikolski Russian mathematician
Nikolai Kapitonowitsch Nikolski Russisch wiskundige
Nikolai Kapitonowitsch Nikolski russischer Mathematiker
Nikolski, N.K.
Nikolski, N.K. 1940
Nikolski, N. K. (Nikolai K.)
Nikolski, Nicolaï
Nikolski Nicolaï 1940....
Nikolski Nicolas 1940....
Nikolski Nikolaï 1940....
Nikolski, Nikolaï K.
Nikolski, Nikolai K. 1940
Nikolʹskî, Nikolaî Kapitonovich
Nikolʹskî, Nikolaî Kapitonovich 1940...
Nikolskï, Nikolaï Kapitonovitch 1940...
Nikolski, Nikolai Kapitonowitsch 1940
Nikolʹskii, N. K.
Nikolʹskiĭ, N. K. 1940
Nikolʹskii, Nikolai K.
Nikolʹskiĭ, Nikolaĭ K. 1940
Nikolʹskiĭ, Nikolaĭ Kapitonovich
Nikolʹskiĭ, Nikolaĭ Kapitonovich 1940
Nikol'skij, N. K.
Nikolʹskij, N. K. 1940
Nikolʹskij, N. K. (Nikolaj Kapitonovich)
Nikolʹskij, Nikolaj 1940
Nikolʹskij, Nikolaj K. 1940
Nikolʹskij, Nikolaj Kapitonovič
Nikolʹskij, Nikolaj Kapitonovič 1940
Nikolʹskij, Nikolaj Kapitonovich
Nikolʹskij, Nikolaj Kapitonovich 1940
Никольский, Н.К 1940
Никольский, Н.К. (Николай Капитонович), 1940
Никольский, Николай Капитонович
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