Best L1 approximation of jump functions in Chebyshev and weak-Chebyshev subspaces of C 0 (a,b)

In this article, we study the problem of the best L1 approximation of jump functions - piecewise continuous functions with a jump discontinuity - in Chebyshev and weak-Chebyshev subspaces of C 0 (a,b). We extend the Hobby-Rice theorem (HR65) into an appropriate framework and prove the unicity of best L1 approximation of jump functions in an even-dimensional Chebyshev subspace. We also apply the results to polynomials and Hermite polynomial splines with fixed knots. Mathematics Subject Classification (2010) 41A10 · 41A15 · 41A50 · 41A52