Best $L_1$ approximation of Heaviside-type functions in Chebyshev and weak-Chebyshev spaces
Functional Analysis
2015-10-27 v3
Abstract
In this article, we study the problem of best approximation of Heaviside-type functions in Chebyshev and weak-Chebyshev spaces. We extend the Hobby-Rice theorem into an appropriate framework and prove the unicity of best approximation of Heaviside-type functions in an even-dimensional Chebyshev space under the condition that the dimension of the subspace composed of the even functions is half the dimension of the whole space. We also apply the results to compute best approximations of Heaviside-type functions by polynomials and Hermite polynomial splines with fixed knots.
Keywords
Cite
@article{arxiv.1407.0228,
title = {Best $L_1$ approximation of Heaviside-type functions in Chebyshev and weak-Chebyshev spaces},
author = {Laurent Gajny and Olivier Gibaru and Eric Nyiri and Shu-Cherng Fang},
journal= {arXiv preprint arXiv:1407.0228},
year = {2015}
}