In this paper we study the Kantorovich sampling type series in a non uniform setting and we obtain a convergence result of our family of discrete operators Swf to the function f in the setting of Musielak-Orlicz spaces. In the language of Signal Processing, this means to reconstruct a signal belonging to a Musielak-Orlicz space (i.e. not necessarily continuous) by means of the family of operators considered that are the Kantorovich versions of the generalized sampling operators. Our theory applies in particular to weighted Orlicz spaces, Orlicz spaces, Lp-spaces, interpolation spaces, exponential spaces and many others. We equip the applications with some graphical example.
Approximation by Means of Kantorovich Generalized Sampling Operators in Musielak-Orlicz spaces
VINTI, Gianluca;
2008
Abstract
In this paper we study the Kantorovich sampling type series in a non uniform setting and we obtain a convergence result of our family of discrete operators Swf to the function f in the setting of Musielak-Orlicz spaces. In the language of Signal Processing, this means to reconstruct a signal belonging to a Musielak-Orlicz space (i.e. not necessarily continuous) by means of the family of operators considered that are the Kantorovich versions of the generalized sampling operators. Our theory applies in particular to weighted Orlicz spaces, Orlicz spaces, Lp-spaces, interpolation spaces, exponential spaces and many others. We equip the applications with some graphical example.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
