Convergence and error estimates for (m,l,s)-splines

In some recent papers, Bouhamidi and Le Mehaute introduced L-m,L-l,L-s-splines as a natural extension of J. Duchon's (m,s)-splines. In the present work, some results on convergence and error estimates for smoothing and interpolating L-m,L-l,L-s-splines (called here (m,l,s)-splines) are given. These results extend those presented in several papers by Duchon, Arcangeli and Lopez de Silanes for (m,s)-splines and also for D-m-splines (i.e. (m,0)-splines).