Semen Kutateladze
Novosibirsk State University, Mathematics, Faculty Member
- Born in 1945 in Leningrad (now St. Petersburg), a senior principal officer of the Sobolev Institute of Mathematics in... moreBorn in 1945 in Leningrad (now St. Petersburg), a senior principal officer of the Sobolev Institute of Mathematics in Novosibirsk and professor at Novosibirsk State University. Authored more than 40 books and 300 papersin functional analysis, convex geometry, optimization, and nonstandardand Boolean valued analysis. A member of the editorial boards ofSiberian Mathematical Journal, Journal of Applied and IndustrialMathematics, Positivity, Mathematical Notes, etc.edit
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1. Discretization is approximation of arbitrary function spaces and operators by their analogs in finite dimensions. Discretization matches the marvelous universal understanding of computational mathematics as the science of finite... more
1. Discretization is approximation of arbitrary function spaces and operators by their analogs in finite dimensions. Discretization matches the marvelous universal understanding of computational mathematics as the science of finite approximations to general (not necessarily metrizable) compacta. This revolutionary and challenging definition was given in the joint talk submitted by S. L. Sobolev, L. A. Lyuster-nik, and L. V. Kantorovich at the Third All-Union Mathematical Congress in 1956. Infinitesimal methods suggest a background, providing new schemes for discretiza-tion of general compact spaces. As an approximation to a compact space we may take an arbitrary internal subset containing all standard elements of the space under approximation. 2. Hypodiscretization of the equation Tx = y, with T: X → Y a bounded linear operator between some Banach spaces X and Y, consists in choosing finite-dimensional vector spaces XN and YN, the corresponding embeddings ıN and N, and some operator...
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This talk overviews the life and mathematical legacy of L. V. Kantorovich (1912–1986). The Appendix contains details on intraction between K-space and the real
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The book treats Boolean valued analysis. This term signifies the technique of studying properties of an arbitrary mathematical object by means of comparison between its representations in two different set-theoretic models whose... more
The book treats Boolean valued analysis. This term signifies the technique of studying properties of an arbitrary mathematical object by means of comparison between its representations in two different set-theoretic models whose construction utilizes principally distinct Boolean algebras. As these models, we usually take the classical Cantorian paradise in the shape of the von Neumann universe and a specially-trimmed Boolean valued universe in which the conventional set-theoretic concepts and propositions acquire bizarre interpretations. Exposition focuses on the fundamental properties of order bounded operators in vector lattices. This volume is intended for the classical analyst seeking new powerful tools and for the model theorist in search of challenging applications of nonstandard models of set theory.
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This collection of articles and essays of the last decade is devoted to science and its place in the modern society. Most attention is paid to the people of science. Several articles reflect the life and contributions of A.D. Alexandrov,... more
This collection of articles and essays of the last decade is devoted to science and its place in the modern society. Most attention is paid to the people of science. Several articles reflect the life and contributions of A.D. Alexandrov, L.V., Kantorovich, N.N. Luzin, S. Mac Lane, S.L. Sobolev, L. Schwartz, and other contemporary scientists. Some room is allotted to the classics of science: Newton, Leibniz, and Euclid. A few articles touch on the history of mathematics, the problems of teaching in higher education, and the criticism of pseudoscience. The book is intended for the wide readership of those interested in science and its people.
This is a collection of a few generalities and conjectures that mostly concern the nature of science and its place in life.
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The book treats Boolean valued analysis. This term signifies the technique of studying properties of an arbitrary mathematical object by means of comparison between its representations in two different set-theoretic models whose... more
The book treats Boolean valued analysis. This term signifies the technique of studying properties of an arbitrary mathematical object by means of comparison between its representations in two different set-theoretic models whose construction utilizes principally distinct Boolean algebras. As these models, we usually take the classical Cantorian paradise in the shape of the von Neumann universe and a specially-trimmed Boolean valued universe in which the conventional set-theoretic concepts and propositions acquire bizarre interpretations. Exposition focuses on the fundamental properties of order bounded operators in vector lattices. This volume is intended for the classical analyst seeking new powerful tools and for the model theorist in search of challenging applications of nonstandard models of set theory.
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This is a survey of some recent applications of Boolean valued analysis to operator theory and harmonic analysis. Under consideration are pseudoembedding operators, the noncommutative Wickstead problem, the Radon-Nikodym Theorem for... more
This is a survey of some recent applications of Boolean valued analysis to operator theory and harmonic analysis. Under consideration are pseudoembedding operators, the noncommutative Wickstead problem, the Radon-Nikodym Theorem for JB-algebras, and the Bochner Theorem for lattice-valued positive definite mappings on locally compact groups.
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This is a biobibliography of Leonid V Kantorovich, a renowed mathematician and economist, with the full list of his publications and reminiscences of his colleagues.
Research Interests: Mathematics and Economics
The book treats Boolean valued analysis. This term signifies the technique of studying properties of an arbitrary mathematical object by means of comparison between its representations in two different set-theoretic models whose... more
The book treats Boolean valued analysis. This term
signifies the technique of studying properties of an arbitrary
mathematical object by means of comparison between its
representations in two different set-theoretic models whose
construction utilizes principally distinct Boolean algebras. As
these models, we usually take the classical Cantorian paradise in the shape of the von Neumann universe and a specially-trimmed Boolean valued universe in which the conventional set-theoretic concepts and propositions acquire bizarre interpretations. Exposition focuses on the fundamental properties of order bounded operators in vector lattices. This volume is intended for the classical analyst seeking new powerful tools and for the model theorist in search of challenging applications of nonstandard models of set theory.
signifies the technique of studying properties of an arbitrary
mathematical object by means of comparison between its
representations in two different set-theoretic models whose
construction utilizes principally distinct Boolean algebras. As
these models, we usually take the classical Cantorian paradise in the shape of the von Neumann universe and a specially-trimmed Boolean valued universe in which the conventional set-theoretic concepts and propositions acquire bizarre interpretations. Exposition focuses on the fundamental properties of order bounded operators in vector lattices. This volume is intended for the classical analyst seeking new powerful tools and for the model theorist in search of challenging applications of nonstandard models of set theory.
Research Interests:
Boolean valued analysis is the technique of studying properties of an arbitrary mathematical object by means of comparison between its representations in two different set-theoretic models whose construction utilizes principally distinct... more
Boolean valued analysis is the technique of studying properties of an arbitrary mathematical object by means of comparison between its representations
in two different set-theoretic models whose construction
utilizes principally distinct Boolean algebras.
As these models, we usually take the classical Cantorian paradise in the shape of the von Neumann universe and a specially-trimmed Boolean valued universe in which the conventional set-theoretic concepts and propositions acquire bizarre interpretations. Usage of two models for studying a single object is a family feature of the so-called nonstandard methods of analysis. For this reason, Boolean valued analysis means an instance of nonstandard analysis in common parlance. This book is in Russia.
in two different set-theoretic models whose construction
utilizes principally distinct Boolean algebras.
As these models, we usually take the classical Cantorian paradise in the shape of the von Neumann universe and a specially-trimmed Boolean valued universe in which the conventional set-theoretic concepts and propositions acquire bizarre interpretations. Usage of two models for studying a single object is a family feature of the so-called nonstandard methods of analysis. For this reason, Boolean valued analysis means an instance of nonstandard analysis in common parlance. This book is in Russia.