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The Markov moment problem and extremal problems / M. G. Krein and A. A. Nudelʹman ; translated by D. Louvish

Auteur principal : Krein, Mark Grigorievich, 1907-1989, AuteurCo-auteur : Nudelman, Adolf Abramovich, 1931-, AuteurAuteur secondaire : Louvish, David, TraducteurType de document : MonographieCollection : Translations of mathematical monographs, 50Langue : anglais.Pays : Etats Unis.Éditeur : Providence : American Mathematical Society, 1977Description : 1 vol. (417 p.) ; 24 cmISBN : 0821845004.Bibliographie : Bibliogr. p. 399-412. Index.Sujet MSC : 42C05, Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis, Orthogonal functions and polynomials, general theory
46-02, Functional analysis, Research exposition (monographs, survey articles)
41A50, Approximations and expansions -- Approximations and expansions, Best approximation, Chebyshev systems
41-02, Approximations and expansions, Research exposition (monographs, survey articles)
En-ligne : Zentralblatt | MathSciNet | AMS
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Trad. de : "Problema momentov Markova i êkstremalʹnye zadachi"

Bibliogr. p. 399-412. Index

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. (source : AMS)

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