Krasnoselʹskiĭ, M. A. (Mark Aleksandrovich) 1920
Overview
Works:  88 works in 379 publications in 5 languages and 4,941 library holdings 

Roles:  Author, Creator, Other, Adapter 
Classifications:  QA320, 517.37 
Publication Timeline
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Most widely held works about
M. A Krasnoselʹskiĭ
 Mark Aleksandrovich Krasnoselʹskiĭ : k 80letii︠u︡ so dni︠a︡ rozhdenii︠a︡( Book )
 Positive solutions of nonlinear problems( Book )
Most widely held works by
M. A Krasnoselʹskiĭ
Topological methods in the theory of nonlinear integral equations by
M. A Krasnoselʹskiĭ(
Book
)
33 editions published between 1963 and 1995 in 3 languages and held by 529 WorldCat member libraries worldwide
33 editions published between 1963 and 1995 in 3 languages and held by 529 WorldCat member libraries worldwide
Convex functions and Orlicz spaces by
M. A Krasnoselʹskiĭ(
Book
)
22 editions published between 1958 and 1962 in English and held by 506 WorldCat member libraries worldwide
22 editions published between 1958 and 1962 in English and held by 506 WorldCat member libraries worldwide
Geometrical methods of nonlinear analysis by
M. A Krasnoselʹskiĭ(
Book
)
16 editions published between 1983 and 2012 in English and German and held by 481 WorldCat member libraries worldwide
16 editions published between 1983 and 2012 in English and German and held by 481 WorldCat member libraries worldwide
Positive solutions of operator equations by
M. A Krasnoselʹskiĭ(
Book
)
16 editions published between 1964 and 1966 in English and Undetermined and held by 409 WorldCat member libraries worldwide
16 editions published between 1964 and 1966 in English and Undetermined and held by 409 WorldCat member libraries worldwide
The operator of translation along the trajectories of differential equations by
M. A Krasnoselʹskiĭ(
Book
)
16 editions published in 1968 in English and Undetermined and held by 403 WorldCat member libraries worldwide
16 editions published in 1968 in English and Undetermined and held by 403 WorldCat member libraries worldwide
Approximate solution of operator equations by
M. A Krasnoselʹskiĭ(
Book
)
16 editions published between 1969 and 1972 in English and Italian and held by 362 WorldCat member libraries worldwide
One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho nov's methods for approximate solution of illposed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni versity on the application of functional analysis to numerical mathe matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters
16 editions published between 1969 and 1972 in English and Italian and held by 362 WorldCat member libraries worldwide
One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho nov's methods for approximate solution of illposed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni versity on the application of functional analysis to numerical mathe matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters
Plane vector fields by
M. A Krasnoselʹskiĭ(
Book
)
21 editions published between 1963 and 1966 in 3 languages and held by 310 WorldCat member libraries worldwide
21 editions published between 1963 and 1966 in 3 languages and held by 310 WorldCat member libraries worldwide
Nonlinear almost periodic oscillations by
M. A Krasnoselʹskiĭ(
Book
)
20 editions published between 1970 and 1973 in 3 languages and held by 276 WorldCat member libraries worldwide
20 editions published between 1970 and 1973 in 3 languages and held by 276 WorldCat member libraries worldwide
Systems with hysteresis by
M. A Krasnoselʹskiĭ(
Book
)
18 editions published between 1983 and 2012 in 3 languages and held by 270 WorldCat member libraries worldwide
Hysteresis phenomena are common in numerous physical, mechanical, ecological and biological systems. They reflect memory effects and process irreversibility. The use of hysteresis operators (hysterons) offers an approach to macroscopic modelling of the dynamics of phase transitions and rheological systems. The applications cover processes in electromagnetism, elastoplasticity and population dynamics in particular. Hysterons are also typical elements of control systems where they represent thermostats and other discontinuous controllers with memory. The book offers the first systematic mathematical treatment of hysteresis nonlinearities. Construction procedures are set up for hysterons in various function spaces, in continuous and discontinuous cases. A general theory of variable hysterons is developed, including identification and stability questions. Both deterministic and nondeterministic hysterons are considered, with applications to the study of feedback systems. Many of the results presented  mostly obtained by the authors and their scientific group  have not been published before. The book is essentially self contained and is addressed both to researchers and advanced students
18 editions published between 1983 and 2012 in 3 languages and held by 270 WorldCat member libraries worldwide
Hysteresis phenomena are common in numerous physical, mechanical, ecological and biological systems. They reflect memory effects and process irreversibility. The use of hysteresis operators (hysterons) offers an approach to macroscopic modelling of the dynamics of phase transitions and rheological systems. The applications cover processes in electromagnetism, elastoplasticity and population dynamics in particular. Hysterons are also typical elements of control systems where they represent thermostats and other discontinuous controllers with memory. The book offers the first systematic mathematical treatment of hysteresis nonlinearities. Construction procedures are set up for hysterons in various function spaces, in continuous and discontinuous cases. A general theory of variable hysterons is developed, including identification and stability questions. Both deterministic and nondeterministic hysterons are considered, with applications to the study of feedback systems. Many of the results presented  mostly obtained by the authors and their scientific group  have not been published before. The book is essentially self contained and is addressed both to researchers and advanced students
Integral operators in spaces of summable functions by
M. A Krasnoselʹskiĭ(
Book
)
12 editions published between 1975 and 1976 in 3 languages and held by 227 WorldCat member libraries worldwide
12 editions published between 1975 and 1976 in 3 languages and held by 227 WorldCat member libraries worldwide
Positive linear systems : the method of positive operators by
M. A Krasnoselʹskiĭ(
Book
)
13 editions published between 1989 and 1990 in 3 languages and held by 142 WorldCat member libraries worldwide
13 editions published between 1989 and 1990 in 3 languages and held by 142 WorldCat member libraries worldwide
Vektorfelder in der Ebene by
M. A Krasnoselʹskiĭ(
Book
)
10 editions published in 1966 in German and Undetermined and held by 140 WorldCat member libraries worldwide
10 editions published in 1966 in German and Undetermined and held by 140 WorldCat member libraries worldwide
Näherungsverfahren zur Lösung von Operatorgleichungen by
M. A Krasnoselʹskiĭ(
Book
)
10 editions published in 1973 in German and Russian and held by 93 WorldCat member libraries worldwide
10 editions published in 1973 in German and Russian and held by 93 WorldCat member libraries worldwide
Topologicheskie metody v teorii nelineĭnykh integralʹnykh uravneniĭ by
M. A Krasnoselʹskiĭ(
Book
)
2 editions published in 1956 in Russian and held by 47 WorldCat member libraries worldwide
2 editions published in 1956 in Russian and held by 47 WorldCat member libraries worldwide
Operator sdviga po traektorii︠a︡m different︠s︡ialʹnykh uravneniĭ by
M. A Krasnoselʹskiĭ(
Book
)
4 editions published in 1966 in Russian and held by 43 WorldCat member libraries worldwide
4 editions published in 1966 in Russian and held by 43 WorldCat member libraries worldwide
Priblizhennoe reshenie operatornykh uravneniĭ by
M. A Krasnoselʹskiĭ(
Book
)
3 editions published in 1969 in Russian and held by 43 WorldCat member libraries worldwide
3 editions published in 1969 in Russian and held by 43 WorldCat member libraries worldwide
Integralʹnye operatory v prostranstvakh summiruemykh funkt︠s︡iĭ by
M. A Krasnoselʹskiĭ(
Book
)
2 editions published in 1966 in Russian and held by 41 WorldCat member libraries worldwide
2 editions published in 1966 in Russian and held by 41 WorldCat member libraries worldwide
Vypuklye funkt︠s︡ii i prostranstva Orlicha by
M. A Krasnoselʹskiĭ(
Book
)
6 editions published in 1958 in Russian and Undetermined and held by 40 WorldCat member libraries worldwide
6 editions published in 1958 in Russian and Undetermined and held by 40 WorldCat member libraries worldwide
Nelineĭnye pochti peridicheskie kolebanii︠a︡ by
M. A Krasnoselʹskiĭ(
Book
)
4 editions published in 1970 in Russian and held by 33 WorldCat member libraries worldwide
4 editions published in 1970 in Russian and held by 33 WorldCat member libraries worldwide
Geometricheskie metody nelineĭnogo analiza by
M. A Krasnoselʹskiĭ(
Book
)
2 editions published in 1975 in Russian and held by 29 WorldCat member libraries worldwide
2 editions published in 1975 in Russian and held by 29 WorldCat member libraries worldwide
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Related Identities
 Zabreĭko, P. P. (Petr Petrovich) 1939
 Rutit︠s︡kiĭ, I︠A︡. B. (I︠A︡kov Bronislavovich)
 Pokrovskiĭ, A. V. (Alekseĭ Vadimovich)
 Burd, V. Sh (Vladimir Shepselevich)
 Kolesov, I︠U︡. S. (I︠U︡riĭ Serafimovich)
 Lifshit︠s︡, E. A. (Evgeniĭ Arkadʹevich)
 Sobolev, A. V. (Aleksandr Vladimirovich)
 Armstrong, A. H. Translator
 Burlak, Jane A. C. Translator Editor
 Vainikko, G. M.
Useful Links
Associated Subjects
Almost periodic functions Approximation theory Boundary value problemsNumerical solutions Calculus, Operational Convex domains Convex functions Differential equations Differential equations, Nonlinear Economics Functional analysis Functions Function spaces Generalized spaces Global analysis (Mathematics) Hysteresis Integral equations Integral operators Iterative methods (Mathematics) Krasnoselʹskiĭ, M. A.(Mark Aleksandrovich), Linear operators Mathematical analysis Mathematical optimization Mathematicians Mathematics Nonlinear operators Nonlinear theories Operator equations Operator equations, Nonlinear Operator equations, NonlinearNumerical solutions Oscillations Positive operators Russia (Federation) Soviet Union Spectrum analysis Summability theory Vector analysis
Alternative Names
Krasnoselski, M.A. 19201997
Krasnoselskii, M. A.
Krasnosel'skii, M. M.
Krasnoselʹskiĭ, Mark 19201997
Krasnosel'skii, Mark A.
Krasnoselʹskiĭ, Mark A. 19201997
Krasnoselʹskiĭ, Mark Aleksandrovich
Krasnoselʹskiĭ, Mark Aleksandrovich 1920
Krasnoselʹskiĭ, Mark Aleksandrovich 19201997
Krasnosel'skij, M. A.
Krasnoselʹskij, M. A. 19201997
Krasnoselʹskij, Mark A. 19201997
Krasnosel'skij, Mark Aleksandrovič
Krasnoselskij, Mark Aleksandrovič 19201997
Krasnosel'skiy, M.A
Krasnoselsky, M. A. 1920
Krasnoselsky, M. A. 19201997
Krasnoselsky, Mark Aleksandrovich 19201997
Krasnosielski, M. A.
Mark Alexandrowitsch Krasnoselski russischer Mathematiker
Mark Krasnosel'skii Mathematician known for nonlinear functional analysis
Mark Krasnosel'skii mathématicien russe
Mark Krasnosel'skii Russisch wiskundige (19201997)
Mark Krasnoselskij
Красносельский, Марк Александрович
Красносельский, Марк Александрович 19201997
Красносельський Марк Олександрович
Languages