Recently, linear positive operators of Bernstein-Schoenberg type, relative to B-splines bases, have been considered. The properties of these operators are derived mainly from the total positivity of normalized B-spline bases. In this paper we shall construct a generalization of the operator considered in [15] by means of normalized totally positive bases generated by a particular class of totally positive scaling functions. Next, we shall study its approximation properties. Our results can be established also for more general sequences of normalized totally positive bases.
Positive refinable operators / Gori, Laura; Pitolli, Francesca; E., Santi. - In: NUMERICAL ALGORITHMS. - ISSN 1017-1398. - STAMPA. - 28:1-4(2001), pp. 199-213. [10.1023/a:1014003102167]
Positive refinable operators
GORI, Laura;PITOLLI, Francesca;
2001
Abstract
Recently, linear positive operators of Bernstein-Schoenberg type, relative to B-splines bases, have been considered. The properties of these operators are derived mainly from the total positivity of normalized B-spline bases. In this paper we shall construct a generalization of the operator considered in [15] by means of normalized totally positive bases generated by a particular class of totally positive scaling functions. Next, we shall study its approximation properties. Our results can be established also for more general sequences of normalized totally positive bases.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
