Approximation results for nonlinear integral operators in modular spaces and applications
Volume 81 / 2003
Annales Polonici Mathematici 81 (2003), 55-71
MSC: 41A35, 46A80, 47G10, 47H30.
DOI: 10.4064/ap81-1-5
Abstract
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.
