We deepen the study of a sequence (C_n )_{n≧1} of positive linear operators, first introduced in [4], that generalize the classical Szász–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 V_l(u)(x)=xu′′(x)+l/2u′(x)(x≧0, l∈[0,2]) on suitable domains of continuous or integrable functions may be approximated by means of iterates of the C_n ’s.
Approximation of some Feller semigroups associated with a modification of Szasz-Mirakjan-Kantorovich operators
LEONESSA, VITA
2013-01-01
Abstract
We deepen the study of a sequence (C_n )_{n≧1} of positive linear operators, first introduced in [4], that generalize the classical Szász–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 V_l(u)(x)=xu′′(x)+l/2u′(x)(x≧0, l∈[0,2]) on suitable domains of continuous or integrable functions may be approximated by means of iterates of the C_n ’s.File in questo prodotto:
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