Abstract
In this article, we study the problem of best L 1 approximation of Heaviside-type functions from Chebyshev and weak-Chebyshev spaces. We extend the Hobby-Rice theorem (Proc. Am. Math. Soc., 16, 665–670, 1965) into an appropriate framework and prove the unicity of best L 1 approximation of Heaviside-type functions from an even-dimensional Chebyshev space under some assumptions on the dimension of the subspaces composed of the odd and even functions. We also apply the results to compute best L 1 approximations of Heaviside-type functions by polynomials and Hermite polynomial splines with fixed knots.
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