Behavior of the beta-splines with values of the parameters beta2 negative (Q1195749)

The authors present some results on the beta-splines when the parameter \(\beta_ 2(i)\) is negative. The cases \(\beta_ 1(i) > 0\) and \(\beta_ 2(i) \geq 0\) have been studied by \textit{T. N. T. Goodman} [J. Approximation Theory 44, 132-153 (1985; Zbl 0569.41010)]. Unfortunately the reader cannot supervise the proofs of the results because these have been already presented by the authors in a previous paper [Comportamento delle funzioni beta-splines con valori del parametro \(\beta_ 2\) negativi, Quaderno 34/1990, Dipartimento di Matematica F. Enriques, Università di Milano (1990)]; here the details of the proofs are omitted. So the paper is only a list of some known results.