Burchard, Hermann G.; Lei, Junjiang Coordinate order of approximation by functional-based approximation operators. (English) Zbl 0829.41021 J. Approximation Theory 82, No. 2, 240-256 (1995). Summary: We study coordinatewise \(L_p\) approximation by a fairly general class of linear operators that includes quasi-interpolants and, like these, is based on a globally supported basis function and a globally supported linear functional of general form with certain mild decay conditions imposed on the basis function and the functional involved. In this quite general setting we show that the approximation power provided by a quasi- interpolant and other functional-based operators is equivalent to the polynomial reproducing property possessed by it. Cited in 5 Documents MSC: 41A35 Approximation by operators (in particular, by integral operators) Keywords:quasi-interpolation PDFBibTeX XMLCite \textit{H. G. Burchard} and \textit{J. Lei}, J. Approx. Theory 82, No. 2, 240--256 (1995; Zbl 0829.41021) Full Text: DOI