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Geometric approximation theory

Alimov, Alexey R.

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Geometric approximation theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometric approximation theory/ by Alexey R. Alimov, Igor' G. Tsar'kov.
Author:	Alimov, Alexey R.
other author:	Tsar'kov, Igor' G.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	1 online resource (xxi, 508 p.) :ill., digital ;24 cm.
[NT 15003449]:	Main notation, definitions, auxillary results, and examples -- Chebyshev alternation theorem, Haar and Mairhuber's theorems -- Best approximation in Euclidean spaces -- Existence and compactness -- Characterization of best approximation -- Convexity of Chebyshev sets and sums -- Connectedness and stability -- Existence of Chebyshev subspaces -- Efimov-Stechkin spaces. Uniform convexity and uniform smoothness. Uniqueness and strong uniqueness of best approximation in uniformly convex spaces -- Solarity of Chebyshev sets -- Rational approximation -- Haar cones and varisolvencity -- Approximation of vector-valued functions -- The Jung constant -- Chebyshev centre of a set -- Width. Approximation by a family of sets -- Approximative properties of arbitrary sets -- Chebyshev systems of functions in the spaces C, Cn, and Lp -- Radon, Helly, and Carathéodory theorems. Decomposition theorem -- Some open problems -- Index.
Contained By:	Springer Nature eBook
Subject:	Approximation theory. -
Online resource:	https://doi.org/10.1007/978-3-030-90951-2
ISBN:	9783030909512

Geometric approximation theory
Alimov, Alexey R.

Geometric approximation theory[electronic resource] /by Alexey R. Alimov, Igor' G. Tsar'kov. - Cham :Springer International Publishing :2021. - 1 online resource (xxi, 508 p.) :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

Main notation, definitions, auxillary results, and examples -- Chebyshev alternation theorem, Haar and Mairhuber's theorems -- Best approximation in Euclidean spaces -- Existence and compactness -- Characterization of best approximation -- Convexity of Chebyshev sets and sums -- Connectedness and stability -- Existence of Chebyshev subspaces -- Efimov-Stechkin spaces. Uniform convexity and uniform smoothness. Uniqueness and strong uniqueness of best approximation in uniformly convex spaces -- Solarity of Chebyshev sets -- Rational approximation -- Haar cones and varisolvencity -- Approximation of vector-valued functions -- The Jung constant -- Chebyshev centre of a set -- Width. Approximation by a family of sets -- Approximative properties of arbitrary sets -- Chebyshev systems of functions in the spaces C, Cn, and Lp -- Radon, Helly, and Carathéodory theorems. Decomposition theorem -- Some open problems -- Index.

This monograph provides a comprehensive introduction to the classical geometric approximation theory, emphasizing important themes related to the theory including uniqueness, stability, and existence of elements of best approximation. It presents a number of fundamental results for both these and related problems, many of which appear for the first time in monograph form. The text also discusses the interrelations between main objects of geometric approximation theory, formulating a number of auxiliary problems for demonstration. Central ideas include the problems of existence and uniqueness of elements of best approximations as well as properties of sets including subspaces of polynomials and splines, classes of rational functions, and abstract subsets of normed linear spaces. The book begins with a brief introduction to geometric approximation theory, progressing through fundamental classical ideas and results as a basis for various approximation sets, suns, and Chebyshev systems. It concludes with a review of approximation by abstract sets and related problems, presenting novel results throughout the section. This text is suitable for both theoretical and applied viewpoints and especially researchers interested in advanced aspects of the field.

ISBN: 9783030909512

Standard No.: 10.1007/978-3-030-90951-2doiSubjects--Topical Terms:

628068
Approximation theory.

LC Class. No.: QA221 / A55 2021

Dewey Class. No.: 511.4

Geometric approximation theory
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100 1 $a Alimov, Alexey R. $3 3538786
245 1 0 $a Geometric approximation theory $h [electronic resource] / $c by Alexey R. Alimov, Igor' G. Tsar'kov.
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300 $a 1 online resource (xxi, 508 p.) : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 2196-9922
505 0 $a Main notation, definitions, auxillary results, and examples -- Chebyshev alternation theorem, Haar and Mairhuber's theorems -- Best approximation in Euclidean spaces -- Existence and compactness -- Characterization of best approximation -- Convexity of Chebyshev sets and sums -- Connectedness and stability -- Existence of Chebyshev subspaces -- Efimov-Stechkin spaces. Uniform convexity and uniform smoothness. Uniqueness and strong uniqueness of best approximation in uniformly convex spaces -- Solarity of Chebyshev sets -- Rational approximation -- Haar cones and varisolvencity -- Approximation of vector-valued functions -- The Jung constant -- Chebyshev centre of a set -- Width. Approximation by a family of sets -- Approximative properties of arbitrary sets -- Chebyshev systems of functions in the spaces C, Cn, and Lp -- Radon, Helly, and Carathéodory theorems. Decomposition theorem -- Some open problems -- Index.
520 $a This monograph provides a comprehensive introduction to the classical geometric approximation theory, emphasizing important themes related to the theory including uniqueness, stability, and existence of elements of best approximation. It presents a number of fundamental results for both these and related problems, many of which appear for the first time in monograph form. The text also discusses the interrelations between main objects of geometric approximation theory, formulating a number of auxiliary problems for demonstration. Central ideas include the problems of existence and uniqueness of elements of best approximations as well as properties of sets including subspaces of polynomials and splines, classes of rational functions, and abstract subsets of normed linear spaces. The book begins with a brief introduction to geometric approximation theory, progressing through fundamental classical ideas and results as a basis for various approximation sets, suns, and Chebyshev systems. It concludes with a review of approximation by abstract sets and related problems, presenting novel results throughout the section. This text is suitable for both theoretical and applied viewpoints and especially researchers interested in advanced aspects of the field.
650 0 $a Approximation theory. $3 628068
650 0 $a Chebyshev systems. $3 705061
650 1 4 $a Approximations and Expansions. $3 897324
700 1 $a Tsar'kov, Igor' G. $3 3538787
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773 0 $t Springer Nature eBook
830 0 $a Springer monographs in mathematics. $3 1535313
856 4 0 $u https://doi.org/10.1007/978-3-030-90951-2
950 $a Mathematics and Statistics (SpringerNature-11649)