Phillips operators preserving arbitrary exponential functions, $e^{at}$, $e^{bt}$

Abstract

In this paper we present a modification of the Phillips operators which reproduces the functions $e^{at}$, $e^{bt}$, $a,b\in\RR$. We study the moments and basic approximation properties for these new operators. For this purpose we adapt several already known result to the particular features of the new sequence that we propose here.