On Complex Valued Functions with Strongly Unique Best Chebyshev Approximation
✍ Scribed by C. Spagl
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 281 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
✦ Synopsis
In contrast to the complex case, the best Chebyshev approximation with respect to a finite-dimensional Haar subspace (V \subset C(Q)) ( (Q) compact) is always strongly unique if all functions are real valued. However, strong uniqueness still holds for complex valued functions (f) with a so-called reference of maximal length. It is known that this class forms an open and dense subset in (C(Q)) if the number of isolated points of (Q) does not exceed (\operatorname{dim} V). In this paper, we show that this result also holds in the space (A(Q)) of functions, analytic in the interior of (Q), if (Q) satisfies a certain regularity condition. 1993 Academic Press, Inc.