Geodesic
Approximation results for nonlinear integral operators in modular spaces and applications
Ilaria Mantellini1 ; Gianluca Vinti1
1Department of Mathematics and Informatics University of Perugia Via Vanvitelli 1 06123 Perugia, Italy
Annales Polonici Mathematici, Tome 81 (2003) no. 1, pp. 55-71
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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

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