Geometric Approximation Theory
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 re...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2021, 2021
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| Edition: | 1st ed. 2021 |
| Series: | Springer Monographs in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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