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

In some recent papers, Bouhamidi and Le Méhauté introduced Lm,l,s-splines as a natural extension of J. Duchonʹs (m,s)-splines. In the present work, some results on convergence and error estimates for smoothing and interpolating Lm,l,s-splines (called here (m,l,s)-splines) are given. These results extend those presented in several papers by Duchon, Arcangéli and Lَpez de Silances for (m,s)-splines and also for Dm-splines (i.e. (m,0)-splines).