High levelm-harmonic cardinal B-splines

We generalize the notion ofm-harmonic cardinal B-spline defined in Rabut, 6c]] to obtain B-splines on an infinite regular grid, which are halfway between elementary B-splines and the Lagrangean cardinal spline function. We give the main properties of these functions: Fourier transform, decay when x , integration,P _k -reproduction (fork<-2m–1) of the associated B-spline approximation, etc. We show that, in some sense, high levelm-harmonic B-splines may be considered as a finer regular approximation of the Dirac distribution than the elementarym-harmonic B-splines are.