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The Markov moment problem and extremal problems

In this book, an extensive circle of questions originating in the classical work of P. L. Chebyshev and A. A. Markov is considered from the more modern point of view. It is shown how results and methods of the generalized moment problem are interlaced with various questions of the geometry of convex...

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Detalles Bibliográficos
Autores principales: Kreĭn, M G, Nudel′man, A A, Louvish, D
Lenguaje:eng
Publicado: American Mathematical Society 1977
Materias:
Acceso en línea:http://cds.cern.ch/record/2623258
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author Kreĭn, M G
Nudel′man, A A
Louvish, D
author_facet Kreĭn, M G
Nudel′man, A A
Louvish, D
author_sort Kreĭn, M G
collection CERN
description In this book, an extensive circle of questions originating in the classical work of P. L. Chebyshev and A. A. Markov is considered from the more modern point of view. It is shown how results and methods of the generalized moment problem are interlaced with various questions of the geometry of convex bodies, algebra, and function theory. From this standpoint, the structure of convex and conical hulls of curves is studied in detail and isoperimetric inequalities for convex hulls are established; a theory of orthogonal and quasiorthogonal polynomials is constructed; problems on limiting values of integrals and on least deviating functions (in various metrics) are generalized and solved; problems in approximation theory and interpolation and extrapolation in various function classes (analytic, absolutely monotone, almost periodic, etc.) are solved, as well as certain problems in optimal control of linear objects.
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spelling cern-26232582021-04-21T18:47:14Zhttp://cds.cern.ch/record/2623258engKreĭn, M GNudel′man, A ALouvish, DThe Markov moment problem and extremal problemsMathematical Physics and MathematicsIn this book, an extensive circle of questions originating in the classical work of P. L. Chebyshev and A. A. Markov is considered from the more modern point of view. It is shown how results and methods of the generalized moment problem are interlaced with various questions of the geometry of convex bodies, algebra, and function theory. From this standpoint, the structure of convex and conical hulls of curves is studied in detail and isoperimetric inequalities for convex hulls are established; a theory of orthogonal and quasiorthogonal polynomials is constructed; problems on limiting values of integrals and on least deviating functions (in various metrics) are generalized and solved; problems in approximation theory and interpolation and extrapolation in various function classes (analytic, absolutely monotone, almost periodic, etc.) are solved, as well as certain problems in optimal control of linear objects.American Mathematical Societyoai:cds.cern.ch:26232581977
spellingShingle Mathematical Physics and Mathematics
Kreĭn, M G
Nudel′man, A A
Louvish, D
The Markov moment problem and extremal problems
title The Markov moment problem and extremal problems
title_full The Markov moment problem and extremal problems
title_fullStr The Markov moment problem and extremal problems
title_full_unstemmed The Markov moment problem and extremal problems
title_short The Markov moment problem and extremal problems
title_sort markov moment problem and extremal problems
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2623258
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AT nudelmanaa markovmomentproblemandextremalproblems
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