Kirillov, A. A. (Aleksandr Aleksandrovich) 1936
Overview
Works:  54 works in 185 publications in 4 languages and 3,698 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor 
Classifications:  QA556, 512.55 
Publication Timeline
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Most widely held works about
A. A Kirillov
 This issue is dedicated to Alexandre A. Kirillov on the occasion of his 70th birthday ( )
 Mackey's method and Kirillov's analysis of representations of nilpotent lie groups by Ali Ansari Astaneh Ali Ansari Astaneh( Book )
Most widely held works by
A. A Kirillov
The method of coordinates
by
I. M Gelʹfand(
Book
)
11 editions published between 1965 and 2002 in English and held by 582 WorldCat member libraries worldwide
11 editions published between 1965 and 2002 in English and held by 582 WorldCat member libraries worldwide
Theorems and problems in functional analysis
by
A. A Kirillov(
Book
)
7 editions published between 1979 and 1988 in 3 languages and held by 455 WorldCat member libraries worldwide
7 editions published between 1979 and 1988 in 3 languages and held by 455 WorldCat member libraries worldwide
Elements of the theory of representations
by
A. A Kirillov(
Book
)
6 editions published in 1976 in English and held by 429 WorldCat member libraries worldwide
6 editions published in 1976 in English and held by 429 WorldCat member libraries worldwide
A tale of two fractals
by
A. A Kirillov(
)
5 editions published in 2013 in English and held by 302 WorldCat member libraries worldwide
Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals helps bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, nonspecialist mathematicians a solid foundation in the theory of fractals. As its title suggests, this book focuses primarily on two fractals: the Sierpiński gasket and the Apollonian gasket. Over the course of the book, they are developed and discussed in various contexts. Along with fundamental definitions and properties, some of the key concepts and approaches covered include * the Laplace operator * harmonic functions * generalized numerical systems * Descartes' theorem * rational paramaterizations * group action on fractals * generalization to multiple dimensions In addition to its explicit goal of providing undergraduate and graduate students with a sound foundation in fractal theory, A Tale of Two Fractals serves to enhance their overall understanding of mathematics by drawing on a wide variety of techniques from other subfields. Furthermore, by virtue of the subject matter, it provides a unique opportunity for students to develop their capacity for recognizing patterns and formulating interesting questions. It is therefore a valuable text not only for any course on fractals or hyperbolic geometry, but also for any survey course with an aim of honing creativeproblemsolving skills
5 editions published in 2013 in English and held by 302 WorldCat member libraries worldwide
Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals helps bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, nonspecialist mathematicians a solid foundation in the theory of fractals. As its title suggests, this book focuses primarily on two fractals: the Sierpiński gasket and the Apollonian gasket. Over the course of the book, they are developed and discussed in various contexts. Along with fundamental definitions and properties, some of the key concepts and approaches covered include * the Laplace operator * harmonic functions * generalized numerical systems * Descartes' theorem * rational paramaterizations * group action on fractals * generalization to multiple dimensions In addition to its explicit goal of providing undergraduate and graduate students with a sound foundation in fractal theory, A Tale of Two Fractals serves to enhance their overall understanding of mathematics by drawing on a wide variety of techniques from other subfields. Furthermore, by virtue of the subject matter, it provides a unique opportunity for students to develop their capacity for recognizing patterns and formulating interesting questions. It is therefore a valuable text not only for any course on fractals or hyperbolic geometry, but also for any survey course with an aim of honing creativeproblemsolving skills
Representation theory and noncommutative harmonic analysis I : fundamental concepts, representations of Virasoro and affine algebras
by
A. A Kirillov(
Book
)
14 editions published between 1994 and 2011 in English and held by 280 WorldCat member libraries worldwide
Part I of this book is a short review of the classical part of representation theory. The main chapters of representation theory are discussed: representations of finite and compact groups, finite and infinitedimensional representations of Lie groups. It is a typical feature of this survey that the structure of the theory is carefully exposed  the reader can easily see the essence of the theory without being overwhelmed by details. The final chapter is devoted to the method of orbits for different types of groups. Part II deals with representation of Virasoro and KacMoody algebra. The second part of the book deals with representations of Virasoro and KacMoody algebra. The wealth of recent results on representations of infinitedimensional groups is presented
14 editions published between 1994 and 2011 in English and held by 280 WorldCat member libraries worldwide
Part I of this book is a short review of the classical part of representation theory. The main chapters of representation theory are discussed: representations of finite and compact groups, finite and infinitedimensional representations of Lie groups. It is a typical feature of this survey that the structure of the theory is carefully exposed  the reader can easily see the essence of the theory without being overwhelmed by details. The final chapter is devoted to the method of orbits for different types of groups. Part II deals with representation of Virasoro and KacMoody algebra. The second part of the book deals with representations of Virasoro and KacMoody algebra. The wealth of recent results on representations of infinitedimensional groups is presented
Representation theory and noncommutative harmonic analysis II
by
A. A Kirillov(
Book
)
13 editions published in 1995 in English and held by 250 WorldCat member libraries worldwide
This EMS volume contains two contributions: the first one, "Harmonic Analysis on Homogeneous Spaces", is written by V.F. Molchanov, the second one, "Representations of Lie Groups and Special Functions", by N. Ya. Vilenkin and A.U. Klimyk. Molchanov focuses on harmonic analysis on semisimple spaces, whereas Vilenkin and Klimyk treat group theoretical methods also with respect to integral transforms. Both contributions are surveys introducing readers to the above topics and preparing them for the study of more specialised literature. This book will be very useful to mathematicians, theoretical physicists and also to chemists dealing with quantum systems
13 editions published in 1995 in English and held by 250 WorldCat member libraries worldwide
This EMS volume contains two contributions: the first one, "Harmonic Analysis on Homogeneous Spaces", is written by V.F. Molchanov, the second one, "Representations of Lie Groups and Special Functions", by N. Ya. Vilenkin and A.U. Klimyk. Molchanov focuses on harmonic analysis on semisimple spaces, whereas Vilenkin and Klimyk treat group theoretical methods also with respect to integral transforms. Both contributions are surveys introducing readers to the above topics and preparing them for the study of more specialised literature. This book will be very useful to mathematicians, theoretical physicists and also to chemists dealing with quantum systems
Lectures on the orbit method
by
A. A Kirillov(
Book
)
4 editions published in 2004 in English and held by 243 WorldCat member libraries worldwide
4 editions published in 2004 in English and held by 243 WorldCat member libraries worldwide
The coordinate method
by
I. M Gelʹfand(
Book
)
21 editions published between 1964 and 1973 in 3 languages and held by 207 WorldCat member libraries worldwide
21 editions published between 1964 and 1973 in 3 languages and held by 207 WorldCat member libraries worldwide
The orbit method in geometry and physics : in honor of A.A. Kirillov
(
Book
)
5 editions published in 2003 in English and held by 200 WorldCat member libraries worldwide
The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and remains a useful and powerful tool in such areas as Lie theory, representation theory, integrable systems, complex geometry, and mathematical physics. Among the distinguished names associated with the orbit method is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), places him as the founder of orbit theory. The original research papers in this volume are written by prominent mathematicians and reflect recent achievements in orbit theory and other closely related areas such as harmonic analysis, classical representation theory, Lie superalgebras, Poisson geometry, and quantization. Contributors: A. Alekseev, J. Alev, V. Baranovksy, R. Brylinski, J. Dixmier, S. Evens, D.R. Farkas, V. Ginzburg, V. Gorbounov, P. Grozman, E. Gutkin, A. Joseph, D. Kazhdan, A.A. Kirillov, B. Kostant, D. Leites, F. Malikov, A. Melnikov, P.W. Michor, Y.A. Neretin, A. Okounkov, G. Olshanski, F. Petrov, A. Polishchuk, W. Rossmann, A. Sergeev, V. Schechtman, I. Shchepochkina. The work will be an invaluable reference for researchers in the above mentioned fields, as well as a useful text for graduate seminars and courses
5 editions published in 2003 in English and held by 200 WorldCat member libraries worldwide
The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and remains a useful and powerful tool in such areas as Lie theory, representation theory, integrable systems, complex geometry, and mathematical physics. Among the distinguished names associated with the orbit method is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), places him as the founder of orbit theory. The original research papers in this volume are written by prominent mathematicians and reflect recent achievements in orbit theory and other closely related areas such as harmonic analysis, classical representation theory, Lie superalgebras, Poisson geometry, and quantization. Contributors: A. Alekseev, J. Alev, V. Baranovksy, R. Brylinski, J. Dixmier, S. Evens, D.R. Farkas, V. Ginzburg, V. Gorbounov, P. Grozman, E. Gutkin, A. Joseph, D. Kazhdan, A.A. Kirillov, B. Kostant, D. Leites, F. Malikov, A. Melnikov, P.W. Michor, Y.A. Neretin, A. Okounkov, G. Olshanski, F. Petrov, A. Polishchuk, W. Rossmann, A. Sergeev, V. Schechtman, I. Shchepochkina. The work will be an invaluable reference for researchers in the above mentioned fields, as well as a useful text for graduate seminars and courses
Kirillov's seminar on representation theory
(
Book
)
4 editions published in 1998 in English and held by 186 WorldCat member libraries worldwide
4 editions published in 1998 in English and held by 186 WorldCat member libraries worldwide
Topics in representation theory
(
Book
)
5 editions published in 1991 in English and held by 140 WorldCat member libraries worldwide
5 editions published in 1991 in English and held by 140 WorldCat member libraries worldwide
Representations of Lie groups and Lie algebras
by Summer School on representation theory(
Book
)
3 editions published in 1985 in English and held by 133 WorldCat member libraries worldwide
3 editions published in 1985 in English and held by 133 WorldCat member libraries worldwide
Eléments de la théorie des représentations
by
A. A Kirillov(
Book
)
15 editions published between 1972 and 1978 in Russian and French and held by 119 WorldCat member libraries worldwide
15 editions published between 1972 and 1978 in Russian and French and held by 119 WorldCat member libraries worldwide
Théorèmes et problèmes d'analyse fonctionnelle
by
A. A Kirillov(
Book
)
3 editions published in 1982 in French and held by 65 WorldCat member libraries worldwide
3 editions published in 1982 in French and held by 65 WorldCat member libraries worldwide
Representation theory and noncommutative harmonic analysis
(
Book
)
8 editions published in 1994 in English and German and held by 22 WorldCat member libraries worldwide
8 editions published in 1994 in English and German and held by 22 WorldCat member libraries worldwide
Izrail M. Gelfand: collected papers
by
I. M Gelʹfand(
Book
)
1 edition published in 1988 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 8 WorldCat member libraries worldwide
Predely
by
A. A Kirillov(
Book
)
4 editions published between 1968 and 1973 in Russian and held by 7 WorldCat member libraries worldwide
4 editions published between 1968 and 1973 in Russian and held by 7 WorldCat member libraries worldwide
Chto takoe chislo?
by
A. A Kirillov(
Book
)
2 editions published in 1993 in Russian and held by 6 WorldCat member libraries worldwide
2 editions published in 1993 in Russian and held by 6 WorldCat member libraries worldwide
Gruppy i algebry Li : algebry Li, svobodnye algebry Li i gruppy Li
by
Nicolas Bourbaki(
Book
)
3 editions published between 1976 and 1986 in Russian and held by 5 WorldCat member libraries worldwide
3 editions published between 1976 and 1986 in Russian and held by 5 WorldCat member libraries worldwide
Lekt︠s︡ii po metodu orbit
by
A. A Kirillov(
Book
)
3 editions published in 2002 in Russian and held by 4 WorldCat member libraries worldwide
3 editions published in 2002 in Russian and held by 4 WorldCat member libraries worldwide
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Associated Subjects
Affine algebraic groups Algebra Algebra, Abstract Calculus Cell aggregationMathematics Chemistry Continuous groups Coordinates Fractals Functional analysis Functions, Special Geometry Global analysis (Mathematics) Global differential geometry Group theory Harmonic analysis Hyperspace KacMoody algebras Lie algebras Lie groups Mackey, George W.(George Whitelaw), Mathematical physics Mathematics Number theory Orbit method Quantum theory Representations of algebras Representations of groups Representations of Lie algebras Representations of Lie groups Topological groups Visualization
Alternative Names
Kirillov, A.
Kirillov, A. A.
Kirillov, A. A. 1936
Kirillov, Aleksandar A.
Kirillov, Aleksandr Aleksandrovič
Kirillov, Aleksandr Aleksandrovič 1936
Kirillov, Aleksandr Aleksandrovich.
Kirillov Aleksandr Aleksandrovich 1936....
Kirillov Aleksandr Aleksandrovitch 1936....
Kirillov, Alexander 1936
Kirillov, Alexander A. 1936
Kirillov, Alexandr A. 1936
Kirillov, Alexandre 1936
Kirillov, Alexandre Alexandrovitch 1936
Kirillow, A. A. 1936
Kirillow, Aleksandr Aleksandrovič 1936
Кириллов, А. А..
Кириллов, Александр Александрович.
キリーロフ, A. A
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