On a max–norm bound for the least–squares spline approximant

0. Introduction Let ξ = (ξi) 1 be a partition of the interval [a, b], i.e., a = ξ1, < · · · < ξ`+1 = b , and let S := IPk,ξ := IPk,ξ ∩ C(m−1)[a, b] denote the collection of piecewise polynomial functions of order k (i.e., of degree < k) with (interior) breakpoints ξ2, . . . , ξl and in C(m−1)[a, b], i.e., satisfying m continuity conditions at each of its interior breakpoints. We are interested in PS , the orthogonal projector onto S with respect to the ordinary inner product