Vilenkin, N. I︠A︡ (Naum I︠A︡kovlevich)
Overview
Works:  194 works in 743 publications in 11 languages and 6,132 library holdings 

Genres:  Popular works 
Roles:  Author, Translator, Creator, Editor, Contributor, Redactor, tra, Other 
Publication Timeline
.
Most widely held works by
N. I︠A︡ Vilenkin
Combinatorics by
N. I︠A︡ Vilenkin(
Book
)
42 editions published between 1969 and 1987 in 7 languages and held by 835 WorldCat member libraries worldwide
Populární formou vysvětluje autor obecná pravidla kombinatoriky, variace, permutace a kombinace, kombinatorické úlohy s omezujícími podmínkami, dále kombinatoriku rozkladů, rekurentní vzorce aj. Výklad ilustruje zajímavýmipříklady z různých oborů a uvádí několik set kombinatorických úloh
42 editions published between 1969 and 1987 in 7 languages and held by 835 WorldCat member libraries worldwide
Populární formou vysvětluje autor obecná pravidla kombinatoriky, variace, permutace a kombinace, kombinatorické úlohy s omezujícími podmínkami, dále kombinatoriku rozkladů, rekurentní vzorce aj. Výklad ilustruje zajímavýmipříklady z různých oborů a uvádí několik set kombinatorických úloh
In search of infinity by
N. I︠A︡ Vilenkin(
Book
)
17 editions published in 1995 in English and held by 812 WorldCat member libraries worldwide
The concept of infinity has been for hundreds of years one of the most fascinating and elusive ideas to tantalize the minds of scholars and lay people alike. The theory of infinite sets lies at the heart of much of mathematics, yet is has produced a series of paradoxes that have led many scholars to doubt the soundness of it foundations. The author of this book presents a popularlevel account of the roads followed by human thought in attempts to understand the idea of the infinite in mathematics and physics. In doing so, he brings to the general reader a deep insight into the nature of the problem and its importance to an understanding of our world. "When I read the first edition of the book, about 20 years ago, I was carried away by Vilenkins storytelling and his ability to bring subtle mathematical ideas down to earth. He stretches our imagination and educates our intuitionThe second edition improves on the first by omission of some routine material about finite properties of sets, and increased attention to infinity. There is a wealth of new material on the position of infinity in human thought, from philosophy to physics, and also on its role in the history of mathematics. In particular, there are now biographical notes on over 100 mathematicians. Abe Shenitzers elegant translation makes this a rare work of literaturea serious mathematical book that will be read from over to cover."John Stillwell, Monash University, Australia
17 editions published in 1995 in English and held by 812 WorldCat member libraries worldwide
The concept of infinity has been for hundreds of years one of the most fascinating and elusive ideas to tantalize the minds of scholars and lay people alike. The theory of infinite sets lies at the heart of much of mathematics, yet is has produced a series of paradoxes that have led many scholars to doubt the soundness of it foundations. The author of this book presents a popularlevel account of the roads followed by human thought in attempts to understand the idea of the infinite in mathematics and physics. In doing so, he brings to the general reader a deep insight into the nature of the problem and its importance to an understanding of our world. "When I read the first edition of the book, about 20 years ago, I was carried away by Vilenkins storytelling and his ability to bring subtle mathematical ideas down to earth. He stretches our imagination and educates our intuitionThe second edition improves on the first by omission of some routine material about finite properties of sets, and increased attention to infinity. There is a wealth of new material on the position of infinity in human thought, from philosophy to physics, and also on its role in the history of mathematics. In particular, there are now biographical notes on over 100 mathematicians. Abe Shenitzers elegant translation makes this a rare work of literaturea serious mathematical book that will be read from over to cover."John Stillwell, Monash University, Australia
Stories about sets by
N. I︠A︡ Vilenkin(
Book
)
32 editions published between 1968 and 2014 in English and held by 723 WorldCat member libraries worldwide
32 editions published between 1968 and 2014 in English and held by 723 WorldCat member libraries worldwide
Special functions and the theory of group representations by
N. I︠A︡ Vilenkin(
Book
)
26 editions published between 1968 and 1998 in English and Undetermined and held by 487 WorldCat member libraries worldwide
26 editions published between 1968 and 1998 in English and Undetermined and held by 487 WorldCat member libraries worldwide
Functional analysis by
Frigyes Riesz(
Book
)
18 editions published between 1967 and 1977 in English and Undetermined and held by 337 WorldCat member libraries worldwide
Classic exposition of modern theories of differentiation and integration and the principal problems and methods of handling integral equations and linear functionals and transformations. Topics include Lebesque and Stieltjes integrals, Hilbert and Banach spaces, selfadjunct transformations, spectral theories for linear transformations of general type, and more
18 editions published between 1967 and 1977 in English and Undetermined and held by 337 WorldCat member libraries worldwide
Classic exposition of modern theories of differentiation and integration and the principal problems and methods of handling integral equations and linear functionals and transformations. Topics include Lebesque and Stieltjes integrals, Hilbert and Banach spaces, selfadjunct transformations, spectral theories for linear transformations of general type, and more
Successive approximation by
N. I︠A︡ Vilenkin(
Book
)
24 editions published in 1964 in 3 languages and held by 337 WorldCat member libraries worldwide
24 editions published in 1964 in 3 languages and held by 337 WorldCat member libraries worldwide
Les distributions by
I. M Gelʹfand(
Book
)
29 editions published between 1962 and 1970 in French and English and held by 178 WorldCat member libraries worldwide
29 editions published between 1962 and 1970 in French and English and held by 178 WorldCat member libraries worldwide
Fonctions spéciales et théories de la représentation des groupes by
N. I︠A︡ Vilenkin(
Book
)
15 editions published in 1969 in 4 languages and held by 165 WorldCat member libraries worldwide
15 editions published in 1969 in 4 languages and held by 165 WorldCat member libraries worldwide
Representation of Lie groups and special functions by
N. I︠A︡ Vilenkin(
Book
)
4 editions published between 1991 and 1993 in English and held by 155 WorldCat member libraries worldwide
4 editions published between 1991 and 1993 in English and held by 155 WorldCat member libraries worldwide
Representation of Lie groups and special functions : recent advances by
N. I︠A︡ Vilenkin(
Book
)
16 editions published between 1995 and 2011 in English and held by 142 WorldCat member libraries worldwide
The present book is a continuation of the threevolume work Representation of Lie Groups and Special Functions by the same authors. Here, they deal with the exposition of the main new developments in the contemporary theory of multivariate special functions, bringing together material that has not been presented in monograph form before. The theory of orthogonal symmetric polynomials (Jack polynomials, Macdonald's polynomials and others) and multivariate hypergeometric functions associated to symmetric polynomials are treated. Multivariate hypergeometric functions, multivariate Jacobi polynomials and hharmonic polynomials connected with root systems and Coxeter groups are introduced. Also, the theory of Gel'fand hypergeometric functions and the theory of multivariate hypergeometric series associated to ClebschGordan coefficients of the unitary group U(n) is given. The volume concludes with an extensive bibliography. For research mathematicians and physicists, postgraduate students in mathematics and mathematical and theoretical physics
16 editions published between 1995 and 2011 in English and held by 142 WorldCat member libraries worldwide
The present book is a continuation of the threevolume work Representation of Lie Groups and Special Functions by the same authors. Here, they deal with the exposition of the main new developments in the contemporary theory of multivariate special functions, bringing together material that has not been presented in monograph form before. The theory of orthogonal symmetric polynomials (Jack polynomials, Macdonald's polynomials and others) and multivariate hypergeometric functions associated to symmetric polynomials are treated. Multivariate hypergeometric functions, multivariate Jacobi polynomials and hharmonic polynomials connected with root systems and Coxeter groups are introduced. Also, the theory of Gel'fand hypergeometric functions and the theory of multivariate hypergeometric series associated to ClebschGordan coefficients of the unitary group U(n) is given. The volume concludes with an extensive bibliography. For research mathematicians and physicists, postgraduate students in mathematics and mathematical and theoretical physics
Generalized functions by
I. M Gelʹfand(
Book
)
30 editions published between 1964 and 2016 in English and Undetermined and held by 134 WorldCat member libraries worldwide
The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The sixvolume collection, Generalized Functions, written by I. M. Gel′fand and coauthors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. The main
30 editions published between 1964 and 2016 in English and Undetermined and held by 134 WorldCat member libraries worldwide
The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The sixvolume collection, Generalized Functions, written by I. M. Gel′fand and coauthors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. The main
Method of successive approximations by
N. I︠A︡ Vilenkin(
Book
)
25 editions published between 1961 and 1980 in 7 languages and held by 126 WorldCat member libraries worldwide
25 editions published between 1961 and 1980 in 7 languages and held by 126 WorldCat member libraries worldwide
Unterhaltsame Mengenlehre by
N. I︠A︡ Vilenkin(
Book
)
15 editions published between 1972 and 1986 in German and held by 90 WorldCat member libraries worldwide
15 editions published between 1972 and 1986 in German and held by 90 WorldCat member libraries worldwide
Representation of Lie groups and special functions by
N. I︠A︡ Vilenkin(
Book
)
28 editions published between 1991 and 2011 in English and held by 70 WorldCat member libraries worldwide
This is the first of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. <br/> This volume deals with the properties of classical orthogonal polynomials and special functions which are related to representations of groups of matrices of second order and of groups of triangular matrices of third order. This material forms the basis of many results concerning classical special functions such as Bessel, MacDonald, Hankel, Whittaker, hypergeometric, and confluent hypergeometric functions, and different classes of orthogonal polynomials, including those having a discrete variable. Many new results are given. <br/> The volume is selfcontained, since an introductory section presents basic required material from algebra, topology, functional analysis and group theory. <br/> For research mathematicians, physicists and engineers
28 editions published between 1991 and 2011 in English and held by 70 WorldCat member libraries worldwide
This is the first of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. <br/> This volume deals with the properties of classical orthogonal polynomials and special functions which are related to representations of groups of matrices of second order and of groups of triangular matrices of third order. This material forms the basis of many results concerning classical special functions such as Bessel, MacDonald, Hankel, Whittaker, hypergeometric, and confluent hypergeometric functions, and different classes of orthogonal polynomials, including those having a discrete variable. Many new results are given. <br/> The volume is selfcontained, since an introductory section presents basic required material from algebra, topology, functional analysis and group theory. <br/> For research mathematicians, physicists and engineers
Representation of Lie groups and special functions by
N. I︠A︡ Vilenkin(
Book
)
18 editions published between 1992 and 2011 in English and held by 68 WorldCat member libraries worldwide
This is the last of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with qanalogs of special functions, quantum groups and algebras (including Hopf algebras), and (representations of) semisimple Lie groups. Also treated are special functions of a matrix argument, representations in the Gel'fandTsetlin basis, and, finally, modular forms, thetafunctions and affine Lie algebras. The volume builds upon results of the previous two volumes, and presents many new results. Subscribers to the complete set of three volumes will be entitled to a discount of 15%
18 editions published between 1992 and 2011 in English and held by 68 WorldCat member libraries worldwide
This is the last of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with qanalogs of special functions, quantum groups and algebras (including Hopf algebras), and (representations of) semisimple Lie groups. Also treated are special functions of a matrix argument, representations in the Gel'fandTsetlin basis, and, finally, modular forms, thetafunctions and affine Lie algebras. The volume builds upon results of the previous two volumes, and presents many new results. Subscribers to the complete set of three volumes will be entitled to a discount of 15%
Generalized functions by
I. M Gelʹfand(
Book
)
17 editions published in 1966 in English and Undetermined and held by 48 WorldCat member libraries worldwide
17 editions published in 1966 in English and Undetermined and held by 48 WorldCat member libraries worldwide
Spet︠s︡ialʹnye funkt︠s︡ii i teorii︠a︡ predstavleniĭ grupp by
N. I︠A︡ Vilenkin(
Book
)
6 editions published between 1965 and 2013 in Russian and English and held by 46 WorldCat member libraries worldwide
6 editions published between 1965 and 2013 in Russian and English and held by 46 WorldCat member libraries worldwide
Representation of Lie groups and special functions by
N. I︠A︡ Vilenkin(
Book
)
12 editions published between 1991 and 1993 in English and held by 46 WorldCat member libraries worldwide
12 editions published between 1991 and 1993 in English and held by 46 WorldCat member libraries worldwide
Quelques applications des mathématiques méthode des approximations successives, gamme simple (structure de l'échelle musicale),
quelques applications de la mécanique aux mathématiques, méthode cinématique dans les problèmes de géométrie by
N. I︠A︡ Vilenkin(
Book
)
11 editions published in 1975 in French and Undetermined and held by 43 WorldCat member libraries worldwide
11 editions published in 1975 in French and Undetermined and held by 43 WorldCat member libraries worldwide
Applications of Harmonic Analysis by
I. M Gelʹfand(
)
1 edition published in 1964 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 1964 in English and held by 0 WorldCat member libraries worldwide
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Related Identities
 Gelʹfand, I. M. (Izrailʹ Moiseevich) Author
 Scripta Technica, inc
 Klimyk, A. U. (Anatoliĭ Ulʹi︠a︡novich) 1939
 Kreĭn, S. G. (Selim Grigorʹevich) 1917 Author Editor
 Votruba, George F. Editor
 Graev, M. I. (Mark Iosifovich) Contributor
 Šilov, Georgij Evgenʹevič (19171975)
 Feinstein, Amiel Translator
 Rideau, Guy Translator
 Vasilach, S. Translator
Useful Links
Associated Subjects
Algebra Approximation theory Astronomy Combinatorial analysis Equations EquationsNumerical solutions Functional analysis Functions Functions, Special Harmonic analysis Hilbert space Infinite Integral transforms Lie groups Logic, Symbolic and mathematical Mathematical physics Mathematics Numerical analysis Quantum groups Representations of groups Representations of Lie groups Set theory Theory of distributions (Functional analysis) Topological groups Transformations (Mathematics)
Alternative Names
Naum Jakowlewitsch Wilenkin russischer Mathematiker
Naum Vilenkin matemático ruso
Naum Vilenkin mathématicien russe
Naum Vilenkin Russian mathematician
Naum Ya. Vilenkin Russisch wiskundige (19201991)
Vilenkin, N.
Vilenkin, N. Â.
Vilenkin, N. IA
Vilenkin, N. J.
Vilenkin, N. J. 19201991
Vilenkin, N. Ja.
Vilenkin, N. Ja 19201991
Vilenkin, N. Y.
Vilenkin N. Ya.
Vilenkin, N. Ya 19201991
Vilenkin Naum Iakovlevich
Vilenkin, Naum I︠A︢kovlevich 19201991
Vilenkin, Naum Jakovlevič.
Vilenkin, Naum Jakovlevič 19201991
Vilenkin, Naum Jakovlevič. [t]
Vilenkin Naum Jakovlevich
Vilenkin, Naum Jakovlevich 19201991
Vilenkin, Naum Yakovlevich.
Vilenkine, N.
Vilenkine, Naoum Iakovlevitch
Vilenkine Naoum Iakovlevitch 1920....
Viļenkins, N. 19201991
Wilenkin N. J.
Wilenkin, N. J. 19201991
Wilenkin, Naum J. 19201991
Wilenkin, Naum Jakovlevič 19201991
Wilenkin, Naum Yakowlewič 1991
Виленкин, Н. Я
Виленкин, Н. Я (Наум Яковлевич)
Виленкин, Наум Яковлевич.
Виленкин, Наум Яковлевич, 19201991
Вілєнкін Наум Якович
Languages
English
(279)
French (49)
German (17)
Russian (17)
Hungarian (3)
Italian (2)
Polish (2)
Multiple languages (2)
Czech (2)
Croatian (1)
Portuguese (1)
French (49)
German (17)
Russian (17)
Hungarian (3)
Italian (2)
Polish (2)
Multiple languages (2)
Czech (2)
Croatian (1)
Portuguese (1)
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