Geodesic
Approximation results for nonlinear integral operators in modular spaces and applications
Ilaria Mantellini1 ; Gianluca Vinti1
1 Department of Mathematics and Informatics University of Perugia Via Vanvitelli 1 06123 Perugia, Italy
Annales Polonici Mathematici, Tome 81 (2003) no. 1, pp. 55-71.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We obtain modular convergence theorems in modular spaces for nets of operators of the form $(T_wf)(s) =\int_{H} K_w (s-h_w (t), f(h_w(t)))\, d\mu_H (t)$, $w>0,$ $s\in G,$ where $G$ and $H$ are topological groups and $\{h_w\}_{w>0}$ is a family of homeomorphisms $h_w :H\rightarrow h_w (H)\subset G.$ Such operators contain, in particular, a nonlinear version of the generalized sampling operators, which have many applications in the theory of signal processing.
DOI : 10.4064/ap81-1-5
Keywords: obtain modular convergence theorems modular spaces nets operators form int s h t where topological groups family homeomorphisms rightarrow subset operators contain particular nonlinear version generalized sampling operators which have many applications theory signal processing

Ilaria Mantellini 1 ; Gianluca Vinti 1

1 Department of Mathematics and Informatics University of Perugia Via Vanvitelli 1 06123 Perugia, Italy 
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Ilaria Mantellini; Gianluca Vinti. Approximation results for nonlinear integral operators
 in modular spaces and applications. Annales Polonici Mathematici, Tome 81 (2003) no. 1, pp. 55-71. doi : 10.4064/ap81-1-5. http://geodesic.mathdoc.fr/articles/10.4064/ap81-1-5/

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