Geometric Approximation Theory

Alexey R. Alimov, Igor’ G. Tsar’kov (Autoren)

Buch | Softcover

XXI, 508 Seiten

2023 | 1st ed. 2021
Springer International Publishing (Verlag)
978-3-030-90953-6 (ISBN)

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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. Itconcludes 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.

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.

Erscheinungsdatum	31.03.2023
Reihe/Serie	Springer Monographs in Mathematics
Zusatzinfo	XXI, 508 p. 21 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	807 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	best approximation • Chebyshev center • Chebyshev set • Chebyshev subspace • Jung constant • Metric projection • nearest point • Sun • width
ISBN-10	3-030-90953-0 / 3030909530
ISBN-13	978-3-030-90953-6 / 9783030909536
Zustand	Neuware