Baskakov operators and their inverses can be expressed as linear differential operators on polynomials. Recurrence relations are given for the computation of these coefficients. They allow the construction of the associated Baskakov quasi-interpolants (abbr. QIs). Then asymptotic results are provided for the determination of the convergence orders of these new quasi-interpolants. Finally some r...

Given a B-spline M on R, s≥ 1 we consider a classical discrete quasi-interpolant Qd written in the form Qdf = ∑ i∈Zs f (i)L(· − i), where L(x) :=∑ j∈JcjM(x− j) for some finite subset J ⊂ Z and cj ∈R. This fundamental function is determined to produce a quasi-interpolation operator exact on the space of polynomials of maximal total degree included in the space spanned by the integer translates o...

In this paper, a second-order Hermite basis of the space of C2quartic splines on the six-directional mesh is constructed and the refinable mask of the basis functions is derived. In addition, the extra parameters of this basis are modified to extend the Hermite interpolating property at the integer lattices by including Lagrange interpolation at the half integers as well. We also formulate a co...