Abstract
The Haar property (see Sect. 2.1), which characterizes the Chebyshev subspace in C(Q), was first formulated for real-valued continuous functions. For real-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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In accordance with the above, a trivial system is an H-system of order zero.
- 2.
A body is a set with nonempty interior.
- 3.
For a definition and basic properties of Efimov–Stechkin spaces, see Sect. 9.1.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Alimov, A.R., Tsar’kov, I.G. (2021). Approximation of Vector-Valued Functions. In: Geometric Approximation Theory. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-90951-2_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-90951-2_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-90950-5
Online ISBN: 978-3-030-90951-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)