Nikolʹskiĭ, N. K. (Nikolaĭ Kapitonovich)
Overview
Works:  52 works in 167 publications in 3 languages and 1,937 library holdings 

Genres:  History Conference papers and proceedings 
Roles:  Author, Editor, Publishing director, Other 
Classifications:  QA329.2, 515.724 
Publication Timeline
.
Most widely held works by
N. K Nikolʹskiĭ
Operators, functions, and systems : an easy reading by
N. K Nikolʹskiĭ(
Book
)
34 editions published in 2002 in English and held by 386 WorldCat member libraries worldwide
34 editions published in 2002 in English and held by 386 WorldCat member libraries worldwide
Kolmogorov's heritage in mathematics by
Éric Charpentier(
Book
)
19 editions published between 2004 and 2007 in English and French and held by 218 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
19 editions published between 2004 and 2007 in English and French and held by 218 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
Investigations in linear operators and function theory by
Nikolaj K Nikolʹskij(
Book
)
in English and held by 191 WorldCat member libraries worldwide
in English and held by 191 WorldCat member libraries worldwide
Toeplitz operators and spectral function theory : essays from the Leningrad Seminar on Operator Theory by Seminar on Operator Theory(
Book
)
9 editions published in 1989 in English and held by 177 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)
9 editions published in 1989 in English and held by 177 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)
Spectral theory of functions and operators by
N. K Nikolʹskiĭ(
Book
)
10 editions published between 1979 and 1983 in English and held by 147 WorldCat member libraries worldwide
10 editions published between 1979 and 1983 in English and held by 147 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
Complex analysis I : entire and meromorphic functions, polyanalytic functions and their generalizations by
A. A Golʹdberg(
Book
)
14 editions published between 1996 and 2000 in English and held by 53 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
14 editions published between 1996 and 2000 in English and held by 53 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
Treatise on the shift operator : spectral function theory by
Nikolaï Kapitonovitch Nikolski(
Book
)
12 editions published between 1980 and 1986 in English and Russian and held by 44 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
12 editions published between 1980 and 1986 in English and Russian and held by 44 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
Izbrannye zadachi vesovoĭ approksimat︠s︡ii i spektralʹnogo analiza by
N. K Nikolʹskiĭ(
Book
)
7 editions published in 1974 in Russian and Undetermined and held by 24 WorldCat member libraries worldwide
7 editions published in 1974 in Russian and Undetermined and held by 24 WorldCat member libraries worldwide
Investigations in linear operators and function theory by
Nikolaj K Nikolʹskij(
Book
)
4 editions published in 1972 in English and held by 11 WorldCat member libraries worldwide
4 editions published in 1972 in English and held by 11 WorldCat member libraries worldwide
Issledovanii︠a︡ po lineĭnym operatoram i teorii funkt︠s︡iĭ : sbornik rabot(
Book
)
2 editions published in 1976 in Russian and held by 10 WorldCat member libraries worldwide
2 editions published in 1976 in Russian and held by 10 WorldCat member libraries worldwide
Spektralʹnai︠a︡ teorii︠a︡ funkt︠s︡iĭ i operatorov : sbornik stateĭ(
Book
)
2 editions published in 1978 in Russian and held by 9 WorldCat member libraries worldwide
2 editions published in 1978 in Russian and held by 9 WorldCat member libraries worldwide
Issledovanii︠a︡ po lineĭnym operatoram i teorii funkt︠s︡iĭ : 99 nereshennykh zadach lineĭnogo i kompleksnogo analiza :
[Sbornik](
Book
)
1 edition published in 1978 in Russian and held by 9 WorldCat member libraries worldwide
1 edition published in 1978 in Russian and held by 9 WorldCat member libraries worldwide
Issledovanija po linejnym operatoram i teorii funkcij : 99 nerešennych zadač linejnogo i kompleksnogo analiza(
Book
)
2 editions published in 1978 in Russian and Undetermined and held by 3 WorldCat member libraries worldwide
2 editions published in 1978 in Russian and Undetermined and held by 3 WorldCat member libraries worldwide
Spektral'naâ teoriâ funkcij i operatorov : sbornik statej(
Book
)
3 editions published between 1978 and 1981 in Russian and held by 3 WorldCat member libraries worldwide
3 editions published between 1978 and 1981 in Russian and held by 3 WorldCat member libraries worldwide
Linear and complex analysis problem book : 199 research problems by
Viktor Petrovich Khavin(
Book
)
1 edition published in 1994 in English and held by 2 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
1 edition published in 1994 in English and held by 2 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
Issledovanija po linejnym operatoram i teorii funkcij(
)
in Russian and held by 2 WorldCat member libraries worldwide
in Russian and held by 2 WorldCat member libraries worldwide
Commutative harmonic analysis. Group methods in commutative harmonic analysis(
Book
)
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
Operators, functions, and systems. an easy reading : Hardy, Hankel, and Toeplitz by
N. K Nikolʹskiĭ(
Book
)
2 editions published in 2002 in English and held by 1 WorldCat member library worldwide
2 editions published in 2002 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Charpentier, Éric Publishing director Author Editor
 Lesne, Annick Publishing director Editor
 Kolmogorov, A. N. (Andreĭ Nikolaevich) 19031987 Author
 Matematicheskiĭ institut im. V.A. Steklova
 Borichev, Alexander A. 1963 Author Editor
 Hartmann, Andreas (19......; mathématicien) Translator
 Khavin, Viktor Petrovich (1933....). Editor
 American Mathematical Society
 Hruŝëv, Sergej Vasilʹevič 1949 ... Writer of accompanying material Editor
 Peller, V. V. Writer of accompanying material
Associated Subjects
Analytic functions Approximation theory Control theory Differentiable dynamical systems Distribution (Probability theory) Fourier analysis Functional analysis Functions Functions, Entire Functions, Meromorphic 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
Nikolski, N. K. (Nikolai K.)
Nikolski, Nicolaï
Nikolski, Nikolai K.
Nikol'skii, N. K.
Nikol'skii, Nikolai K.
Nikolʹskiĭ, Nikolaĭ Kapitonovich
Nikol'skii Nikolai Kapitonovich 1940....
Nikol'skij, N. K.
Nikolʹskij, N. K. (Nikolaj Kapitonovich)
Nikolʹskij, Nikolaj Kapitonovich
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