A unifying approach to convergence of linear sampling type operators in Orlicz spaces

Abstract

In this paper we give a unified approach to the study of the convergence of a general family of linear sampling type operators which includes several operators very useful in signal reconstruction. We study both the pointwise and uniform convergence and the modular one in the general setting of Orlicz spaces. This creates the possibility of covering several settings such as $L^p$-spaces, the interpolation spaces, the exponential spaces and many others.