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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Painstaking

https://doi.org/10.1007/978-3-030-34702-4ple, of approximation by rational fractions, splines with free knots, and exponential sums (see Sect.?. and Chap.?.). For such sets?., approximative properties of existence, uniqueness, and approximative compactness are of special importance.

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要素

Convexity of Chebyshev Sets and Suns,owing 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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ALERT

Approximation of Vector-Valued Functions,al-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 to be less simple.

BLAZE

Chebyshev Centre of a Set. The Problem of Simultaneous Approximation of a Class by a Singleton Set,ce. In this chapter, we consider the problem of approximating a?set by a?class of sets. In this problem, it is not only the evaluation of the approximation that is important, but also the?set that best approximates this class (an optimal set).

Dictation

Approximative Properties of Arbitrary Sets in Normed Linear Spaces. Almost Chebyshev Sets and Sets ple, of approximation by rational fractions, splines with free knots, and exponential sums (see Sect.?. and Chap.?.). For such sets?., approximative properties of existence, uniqueness, and approximative compactness are of special importance.

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