Nikolʹskiĭ, N. K. (Nikolaĭ Kapitonovich)
Overview
Works:  119 works in 492 publications in 4 languages and 6,777 library holdings 

Genres:  Conference papers and proceedings History 
Roles:  Author, Editor, Publishing director, Other, ed, Honoree, Thesis advisor 
Classifications:  QA403, 515.2433 
Publication Timeline
.
Most widely held works by
N. K Nikolʹskiĭ
Commutative harmonic analysis I : general survey, classical aspects by
Viktor Petrovich Khavin(
Book
)
97 editions published between 1987 and 2011 in 3 languages and held by 1,046 WorldCat member libraries worldwide
This EMS volume shows the great power provided by modern harmonic analysis, not only in mathematics, but also in mathematical physics and engineering. Aimed at a reader who has learned the principles of harmonic analysis, this book is intended to provide a variety of perspectives on this important classical subject. The authors have written an outstanding book which distinguishes itself by the authors' excellent expository style. It can be useful for the expert in one area of harmonic analysis who wishes to obtain broader knowledge of other aspects of the subject and also by graduate students in other areas of mathematics who wish a general but rigorous introduction to the subject
97 editions published between 1987 and 2011 in 3 languages and held by 1,046 WorldCat member libraries worldwide
This EMS volume shows the great power provided by modern harmonic analysis, not only in mathematics, but also in mathematical physics and engineering. Aimed at a reader who has learned the principles of harmonic analysis, this book is intended to provide a variety of perspectives on this important classical subject. The authors have written an outstanding book which distinguishes itself by the authors' excellent expository style. It can be useful for the expert in one area of harmonic analysis who wishes to obtain broader knowledge of other aspects of the subject and also by graduate students in other areas of mathematics who wish a general but rigorous introduction to the subject
Treatise on the shift operator : spectral function theory by
N. K Nikolʹskiĭ(
Book
)
20 editions published between 1985 and 2012 in English and held by 389 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
20 editions published between 1985 and 2012 in English and held by 389 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
)
14 editions published in 1984 in 3 languages and held by 368 WorldCat member libraries worldwide
14 editions published in 1984 in 3 languages and held by 368 WorldCat member libraries worldwide
Functional analysis I : linear functional analysis by
I︠U︡. I Li︠u︡bich(
Book
)
29 editions published between 1991 and 1992 in English and held by 364 WorldCat member libraries worldwide
The twentieth century view of the analysis of functions is dominated by the study of classes of functions, as contrasted with the older emphasis on the study of individual functions. Operator theory has had a similar evolution, leading to a primary role for families of operators. This volume of the Encyclopaedia covers the origins, development and applications of linear functional analysis, explaining along the way how one is led naturally to the modern approach. The book consists of two chapters, the first of which deals with classical aspects of the subject, while the second presents the abstract modern theory and some of its applications. Both chapters are divided into sections which are devoted to individual topics. For each topic the origins are traced, the principal definitions and results are stated and illustrative examples for theory and applications are given. Usually proofs are omitted, although certain sections of Chapter 2 do contain some quite detailed proofs. The classical concrete problems of Chapter 1 provide motivation and examples, as well as a technical foundation, for the theory in Chapter 2
29 editions published between 1991 and 1992 in English and held by 364 WorldCat member libraries worldwide
The twentieth century view of the analysis of functions is dominated by the study of classes of functions, as contrasted with the older emphasis on the study of individual functions. Operator theory has had a similar evolution, leading to a primary role for families of operators. This volume of the Encyclopaedia covers the origins, development and applications of linear functional analysis, explaining along the way how one is led naturally to the modern approach. The book consists of two chapters, the first of which deals with classical aspects of the subject, while the second presents the abstract modern theory and some of its applications. Both chapters are divided into sections which are devoted to individual topics. For each topic the origins are traced, the principal definitions and results are stated and illustrative examples for theory and applications are given. Usually proofs are omitted, although certain sections of Chapter 2 do contain some quite detailed proofs. The classical concrete problems of Chapter 1 provide motivation and examples, as well as a technical foundation, for the theory in Chapter 2
Complex analysis and spectral theory seminar : Leningrad 197980 by
V. P Havin(
Book
)
18 editions published between 1981 and 2008 in English and held by 354 WorldCat member libraries worldwide
18 editions published between 1981 and 2008 in English and held by 354 WorldCat member libraries worldwide
Kolmogorov's heritage in mathematics by
Éric Charpentier(
Book
)
17 editions published between 2004 and 2007 in English and French and held by 219 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 K
17 editions published between 2004 and 2007 in English and French and held by 219 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 K
Selected problems of weighted approximation and spectral analysis by
N. K Nikolʹskiĭ(
Book
)
8 editions published in 1976 in English and held by 197 WorldCat member libraries worldwide
8 editions published in 1976 in English and held by 197 WorldCat member libraries worldwide
Investigations in linear operators and function theory by
N. K Nikolʹskiĭ(
Book
)
3 editions published in 1972 in English and held by 185 WorldCat member libraries worldwide
3 editions published in 1972 in English and held by 185 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 182 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 182 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 by
I Gohberg(
Book
)
11 editions published between 1991 and 2000 in English and held by 170 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 170 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
Spectral theory of functions and operators(
Book
)
in English and held by 124 WorldCat member libraries worldwide
in English and held by 124 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
)
7 editions published in 2001 in English and held by 98 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
7 editions published in 2001 in English and held by 98 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
)
2 editions published in 2003 in French and held by 88 WorldCat member libraries worldwide
2 editions published in 2003 in French and held by 88 WorldCat member libraries worldwide
Leçons de mathématiques d'aujourd'hui by
JeanPierre Kahane(
Book
)
5 editions published in 2000 in French and held by 82 WorldCat member libraries worldwide
5 editions published in 2000 in French and held by 82 WorldCat member libraries worldwide
Leçons de mathématiques d'aujourd'hui by
B Perthame(
Book
)
4 editions published in 2007 in French and held by 81 WorldCat member libraries worldwide
4 editions published in 2007 in French and held by 81 WorldCat member libraries worldwide
Éléments d'analyse avancée by
N. K Nikolʹskiĭ(
Book
)
1 edition published in 2012 in French and held by 42 WorldCat member libraries worldwide
1 edition published in 2012 in French and held by 42 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
 Kolmogorov, A. N. (Andreĭ Nikolaevich) 19031987 Author
 Khrushchev, S. V. Writer of accompanying material Editor
 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) Group theory 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 Mathematical physics Mathematics Operator theory Shift operators (Operator theory) Sidon sets Singular integrals Spectral theory (Mathematics) Toeplitz operators Topological groups Topology
Alternative Names
Nikolai Kapitonowitsch Nikolski mathématicien russe
Nikolai Kapitonowitsch Nikolski Russian mathematician
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
Nikolskii, N.K.
Nikolʹskiĭ, N. K. 1940
Nikolʹskii, Nikolai K.
Nikolʹskiĭ, Nikolaĭ K. 1940
Nikolʹskiĭ, Nikolaĭ Kapitonovich
Nikolʹskiĭ, Nikolaĭ Kapitonovich 1940
Nikolʹskij, 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
Н.К. Никольский
Никольский, Н.К. (Николай Капитонович), 1940
Никольский, Николай Капитонович
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