Approximation of some Feller semigroups associated with a modification of Szasz-Mirakjan-Kantorovich operators

被引：2
|
作者：
Cappelletti Montano, M. [1 ]
Leonessa, V. [2 ]
机构：
[1] Univ Bari A Moro, Dipartimento Matemat, I-70125 Bari, Italy
[2] Univ Basilicata, Dipartimento Matemat & Informat, I-85100 Potenza, Italy
来源：
ACTA MATHEMATICA HUNGARICA | 2013年 / 139卷 / 03期
关键词：
positive approximation process; Szasz-Mirakjan-Kantorovich operator; asymptotic formula; degenerate second order differential operator; iterate of operators; Feller semigroup; approximation of semigroups;
D O I：
10.1007/s10474-012-0267-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We deepen the study of a sequence (C (n) ) (na parts per thousand 1) of positive linear operators, first introduced in [4], that generalize the classical Szasz-Mirakjan-Kantorovich operators. In particular, we present some qualitative properties and an asymptotic formula for such a sequence. Moreover, we prove that, under suitable assumptions, the C (0)-semigroups generated by the second order differential operator on suitable domains of continuous or integrable functions may be approximated by means of iterates of the C (n) 's.
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页码：255 / 275
页数：21
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