A general approach to the convergence theorems of generalized sampling series

Abstract

Modular convergence theorems in Orlicz spaces for nets of operators of the form , w>0, s∊G, where G and H are topological groups and {h_w} a family of homeomorphisms , are given. As applications, in the particular case of G = (ℝ,+), H = (z,+), K_w(z)=K(wz), we obtain modular convergence theorems in a clasical Orlicz sapce for the generalized sampling series of ,s∊ℝ, w>0.

Keywords:

• Orlicz space
• Generalized sampling seris
• Topological groups
• Modular convergence
• Jensen's inequality

^∗Dipartimento di Matematica, Universitá degli Studi di Perugia, Via Vanvitelli, 1 06123-Perugia, Italia-Fax:[phone]. [email protected]

^∗Dipartimento di Matematica, Universitá degli Studi di Perugia, Via Vanvitelli, 1 06123-Perugia, Italia-Fax:[phone]. [email protected]

Notes

^∗Dipartimento di Matematica, Universitá degli Studi di Perugia, Via Vanvitelli, 1 06123-Perugia, Italia-Fax:[phone]. [email protected]

Additional information

Notes on contributors

Bardaro Carlo