Kusraev, A. G.
Overview
Works:  46 works in 105 publications in 3 languages and 784 library holdings 

Genres:  History Conference proceedings 
Roles:  Author, Editor 
Classifications:  QA299.82, 515 
Publication Timeline
.
Most widely held works by
A. G Kusraev
Nonstandard methods of analysis
by
A. G Kusraev(
Book
)
11 editions published in 1994 in English and held by 143 WorldCat member libraries worldwide
<Em>Nonstandard Methods of Analysis</em> is concerned with the main trends in this field; infinitesimal analysis and Booleanvalued analysis. The methods that have been developed in the last twentyfive years are explained in detail, and are collected in book form for the first time. Special attention is paid to general principles and fundamentals of formalisms for infinitesimals as well as to the technique of descents and ascents in a Booleanvalued universe. The book also includes various novel applications of nonstandard methods to ordered algebraic systems, vector lattices, subdifferentials, convex programming etc. that have been developed in recent years. <br/> For graduate students, postgraduates and all researchers interested in applying nonstandard methods in their work. <br/>
11 editions published in 1994 in English and held by 143 WorldCat member libraries worldwide
<Em>Nonstandard Methods of Analysis</em> is concerned with the main trends in this field; infinitesimal analysis and Booleanvalued analysis. The methods that have been developed in the last twentyfive years are explained in detail, and are collected in book form for the first time. Special attention is paid to general principles and fundamentals of formalisms for infinitesimals as well as to the technique of descents and ascents in a Booleanvalued universe. The book also includes various novel applications of nonstandard methods to ordered algebraic systems, vector lattices, subdifferentials, convex programming etc. that have been developed in recent years. <br/> For graduate students, postgraduates and all researchers interested in applying nonstandard methods in their work. <br/>
Subdifferentials : theory and applications
by
A. G Kusraev(
Book
)
7 editions published in 1995 in English and Italian and held by 120 WorldCat member libraries worldwide
7 editions published in 1995 in English and Italian and held by 120 WorldCat member libraries worldwide
Infinitesimal analysis
by
E. I Gordon(
Book
)
10 editions published between 2001 and 2011 in English and Russian and held by 119 WorldCat member libraries worldwide
Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing uptodate methods of monadology and hyperapproximation. This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0792359216 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0792366190
10 editions published between 2001 and 2011 in English and Russian and held by 119 WorldCat member libraries worldwide
Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing uptodate methods of monadology and hyperapproximation. This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0792359216 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0792366190
Boolean valued analysis
by
A. G Kusraev(
Book
)
7 editions published in 1999 in English and held by 112 WorldCat member libraries worldwide
Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different settheoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the socalled nonstandard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vectorfunctions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models
7 editions published in 1999 in English and held by 112 WorldCat member libraries worldwide
Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different settheoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the socalled nonstandard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vectorfunctions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models
Dominated operators
by
A. G Kusraev(
Book
)
3 editions published between 2000 and 2011 in English and held by 86 WorldCat member libraries worldwide
This book presents the main results of the last fifteen years on dominated operators, demonstrating a welldeveloped theory with a wide range of applications. The exposition focuses on the fundamental properties of dominated operators with special emphasis on their particular classes: integral and pseudointegral operators, disjointness preserving and decomposable operators, summing and cyclically compact operators, etc. Audience: This volume will be of interest to postgraduate students and researchers whose work involves geometric functional analysis, operator theory, vector lattices, measure and integration theory, and mathematical logic and foundations
3 editions published between 2000 and 2011 in English and held by 86 WorldCat member libraries worldwide
This book presents the main results of the last fifteen years on dominated operators, demonstrating a welldeveloped theory with a wide range of applications. The exposition focuses on the fundamental properties of dominated operators with special emphasis on their particular classes: integral and pseudointegral operators, disjointness preserving and decomposable operators, summing and cyclically compact operators, etc. Audience: This volume will be of interest to postgraduate students and researchers whose work involves geometric functional analysis, operator theory, vector lattices, measure and integration theory, and mathematical logic and foundations
Subdifferentials: Theory and Applications
by
A. G Kusraev(
)
4 editions published in 1995 in English and held by 23 WorldCat member libraries worldwide
This monograph presents the most important results of a new branch of functional analysis: subdifferential calculus and its applications. New tools and techniques of convex and nonsmooth analysis are presented, such as Kantorovich spaces, vector duality, Booleanvalued and infinitesimal versions of nonstandard analysis, etc., covering a wide range of topics. <br/> This volume fills the gap between the theoretical core of modern functional analysis and its applicable sections, such as optimization, optimal control, mathematical programming, economics and related subjects. <br/> The material in this book will be of interest to theoretical mathematicians looking for possible new applications and applied mathematicians seeking powerful contemporary theoretical methods. <br/>
4 editions published in 1995 in English and held by 23 WorldCat member libraries worldwide
This monograph presents the most important results of a new branch of functional analysis: subdifferential calculus and its applications. New tools and techniques of convex and nonsmooth analysis are presented, such as Kantorovich spaces, vector duality, Booleanvalued and infinitesimal versions of nonstandard analysis, etc., covering a wide range of topics. <br/> This volume fills the gap between the theoretical core of modern functional analysis and its applicable sections, such as optimization, optimal control, mathematical programming, economics and related subjects. <br/> The material in this book will be of interest to theoretical mathematicians looking for possible new applications and applied mathematicians seeking powerful contemporary theoretical methods. <br/>
Vektornai︠a︡ dvoĭstvennostʹ i ee prilozhenii︠a︡
by
A. G Kusraev(
Book
)
4 editions published in 1985 in Russian and held by 22 WorldCat member libraries worldwide
4 editions published in 1985 in Russian and held by 22 WorldCat member libraries worldwide
Subdifferent︠s︡ialʹnoe ischislenie
by
A. G Kusraev(
Book
)
3 editions published in 1987 in Russian and held by 21 WorldCat member libraries worldwide
3 editions published in 1987 in Russian and held by 21 WorldCat member libraries worldwide
Nestandartnye metody analiza
by
A. G Kusraev(
Book
)
2 editions published in 1990 in Russian and held by 19 WorldCat member libraries worldwide
2 editions published in 1990 in Russian and held by 19 WorldCat member libraries worldwide
Subdifferent︠s︡ialy : teorii︠a︡ i prilozhenii︠a︡
by
A. G Kusraev(
Book
)
3 editions published in 1992 in Russian and held by 15 WorldCat member libraries worldwide
3 editions published in 1992 in Russian and held by 15 WorldCat member libraries worldwide
Nekotorye voprosy teorii vektornykh mer
by
A. G Kusraev(
Book
)
4 editions published in 1988 in Russian and held by 12 WorldCat member libraries worldwide
4 editions published in 1988 in Russian and held by 12 WorldCat member libraries worldwide
Kavkaz spusti︠a︡ 20 let : geopolitika i problemy bezopasnosti, trudy mezhdunarodnoĭ nauchnoĭ konferent︠s︡ii, VladikavkazT︠S︡khinval, 2030 ii︠u︡ni︠a︡ 2011 g.
by Mezhdunarodnyĭ nauchnyĭ forum "Kavkaz spusti︠a︡ 20 let: geopolitika i problemy bezopasnosti"(
Book
)
1 edition published in 2011 in Russian and held by 11 WorldCat member libraries worldwide
1 edition published in 2011 in Russian and held by 11 WorldCat member libraries worldwide
Ėlementy bulevoznachnogo analiza
by
A. G Kusraev(
Book
)
3 editions published in 1987 in Russian and held by 9 WorldCat member libraries worldwide
3 editions published in 1987 in Russian and held by 9 WorldCat member libraries worldwide
Issledovanii︠a︡ po funkt︠s︡ionalʹnomu analizu i ego prilozhenii︠a︡m = Studies on functional analysis and its applications
(
Book
)
3 editions published in 2006 in Russian and held by 8 WorldCat member libraries worldwide
3 editions published in 2006 in Russian and held by 8 WorldCat member libraries worldwide
Mazhoriruemye operatory
by
A. G Kusraev(
Book
)
3 editions published in 2003 in Russian and Undetermined and held by 8 WorldCat member libraries worldwide
3 editions published in 2003 in Russian and Undetermined and held by 8 WorldCat member libraries worldwide
Subdifferencialʹnoe isčislenie
by
A. G Kusraev(
Book
)
4 editions published between 1983 and 1987 in Russian and Undetermined and held by 6 WorldCat member libraries worldwide
4 editions published between 1983 and 1987 in Russian and Undetermined and held by 6 WorldCat member libraries worldwide
Vektornaja dvojstvennostʹ i ee priloženija
by
A. G Kusraev(
Book
)
2 editions published in 1985 in Russian and held by 5 WorldCat member libraries worldwide
2 editions published in 1985 in Russian and held by 5 WorldCat member libraries worldwide
Subdifferent︠s︡ialʹnoe ischislenie : teorii︠a︡ i prilozhenii︠a︡
by
A. G Kusraev(
Book
)
2 editions published in 2007 in Russian and held by 5 WorldCat member libraries worldwide
2 editions published in 2007 in Russian and held by 5 WorldCat member libraries worldwide
Bulevoznachnyĭ analiz
by
A. G Kusraev(
Book
)
1 edition published in 1999 in Russian and held by 4 WorldCat member libraries worldwide
1 edition published in 1999 in Russian and held by 4 WorldCat member libraries worldwide
Vvedenie b bulevoznachnyĭ analiz
by
A. G Kusraev(
Book
)
1 edition published in 2005 in Russian and held by 4 WorldCat member libraries worldwide
1 edition published in 2005 in Russian and held by 4 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Kutateladze, S. S. (Semen Samsonovich) Honoree Editor
 Gordon, E. I. (Evgenii Izrailevich) 1949 Author
 Kutateladze, Samson Semenovich
 Reshetni︠a︡k, I︠U︡riĭ Grigorʹevich
 Aleksandrov, A. D. (Aleksandr Danilovich) 19121999
 Kanukova, Z. V. (Zalina Vladimirovna)
 Krylov, A. B. (Aleksandr Borisovich)
 Mali︠u︡gin, S. A. (Sergeĭ Artemʹevich)
 Kutateladze, S. S.
 Institut matematiki im. S.L. Soboleva Editor
Associated Subjects
Algebra, Boolean Caucasus Convex functions Differential calculus Differential equations, PartialNumerical solutions Discrete groups Functional analysis Functional equations Geopolitics Lattice theory Logic, Symbolic and mathematical Mathematical optimization Mathematics National security Nonsmooth optimization Nonstandard mathematical analysis Operator theory Riesz spaces Subdifferentials Topology Vector spaces Vector valued functions Vectorvalued measures