On the prolongation of convex functions of higher order


This is the paper where the B-splines on nonuniform grid are introduced and studied for the first time. The recurrence formula and knot insertion formula are also dealt with.


Original title (in French)

Sur le prolongement des fonctions convexes d’ordre superieur


B-splines; recurrence formula; knot insertion formula.

Cite this paper as

T. Popoviciu, Sur le prolongement des fonctions convexes d’ordre superieur, Bull. Math. Soc. Roum. Sci., 36 (1934) no. 1, pp. 75-108.


About this paper


Bulletin mathématique de la Société Roumaine des Sciences

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Notes on this paper

The results of T. Popoviciu were acknowledged by Carl de Boor and Alan Pinkus in their paper from 2003

  • A. Pinkus and C. de Boor, The B-spline recurrence relations of Chakalov and of Popoviciu, J. Approx. Theory, 124 (2003) no. 1, pp. 115-123, doi: 10.1016/S0021-9045(03)00117-5

see also the paper of Carl de Boor from 2015

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