Titlebook: Geometric Approximation Theory; Alexey R. Alimov,Igor’ G. Tsar’kov Book 2021 The Editor(s) (if applicable) and The Author(s), under exclus

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Discursive Approaches to Language Policyes .(.), we give several results that either characterize or give sufficient conditions for the existence of Chebyshev subspaces in?.(.). Among such conditions, we mention de la Vallée Poussin’s estimates (see Sect.?.), the Haar characterization property (see?Sect.?.), and Mairhuber’s theorem (see S

PANT

https://doi.org/10.1007/978-3-030-55038-7of a?finite-dimensional subspace (or a?convex set). We present two fundamental results on approximation by convex sets in the inner-product setting?—?the Kolmogorov criterion of best approximation and Phelps’s criterion for convexity of a?Chebyshev set in a?Euclidean space in terms of the Lipschitz

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https://doi.org/10.1007/978-981-19-4097-2owing fact important for applications: in corresponding spaces, a?nonconvex set cannot be a?Chebyshev set. As a?corollary, at some point either the existence or the uniqueness property is not satisfied. Results of this kind can be useful in solving extremal problems.

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Ryan Evely Gildersleeve,Katie Kleinhesselink uniqueness sets, and so?on). By structural characteristics of sets one usually understands properties of linearity, finite-dimensionality, convexity, connectedness of various kinds, and smoothness of sets. From results of such kind one may derive necessary and sufficient conditions for a?set to hav

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https://doi.org/10.1057/9781137487339pproximative properties of more general subspaces stems from consideration of Chebyshev (Haar) systems of functions that extend the classical Chebyshev system composed of polynomials of degree at most?. (see Chap.?2). Of course, every space?. contains trivial Chebyshev subspaces: . and ..

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frequently encountered in various extreme problems. Properties of Haar cones, as well as uniqueness and strong uniqueness of best approximation by Haar cones, are discussed in Sect.?.. The alternation theorem for Haar cones is given in?Sect.?.. Next in ., we discuss the property of varisolvency, wh

分離

https://doi.org/10.1007/978-1-4842-3267-5al-valued functions, approximation by Chebyshev subspaces was found to be closely related to various problems in interpolation, uniqueness, and the number of zeros in nontrivial polynomials (the generalized Haar property). For vector-valued functions, the relation between such properties turned out