The Markov moment problem and extremal problems / M. G. Krein and A. A. Nudelʹman ; translated by D. LouvishType 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.ISSN: 0065-9282.Bibliographie : Bibliogr. p. 399-412. Index.Sujet MSC : 42C05, Nontrigonometric harmonic analysis, Orthogonal functions and polynomials, general theory
46-02, Research exposition (monographs, survey articles) pertaining to functional analysis
41A50, Approximations and expansions, Best approximation, Chebyshev systems
41-02, Research exposition (monographs, survey articles) pertaining to approximations and expansionsEn-ligne : Zentralblatt | MathSciNet | AMS Item type: Monographie
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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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