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Approximation results for nonlinear integral operators in modular spaces and applications. (English) Zbl 1019.41013
Author’s abstract: We obtain modular convergence theorems in modular spaces for nets of operators of the form \[ (T_wf)(s)= \int_HK_w \biggl( s-h_w(t), f\bigl(h_w(t) \bigr)\biggr) d\mu_H(t), \;w>0,s\in G, \] where \(G\) and \(H\) are topological groups and \(\{h_w\}_{w>0}\) is a family of homeomorphisms \(h_w:H\to h_w(H) \subset G\). Such operators contain, in particular, a nonlinear version of the generalized sampling operators, which have many applications in the theory of signal processing.

41A35 Approximation by operators (in particular, by integral operators)
46A80 Modular spaces
47G10 Integral operators
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiń≠, Uryson, etc.)
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