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Approximation results for nonlinear integral operators in modular spaces and applications

Ilaria Mantellini, Gianluca Vinti (2003)

Annales Polonici Mathematici

We obtain modular convergence theorems in modular spaces for nets of operators of the form ( T w f ) ( s ) = H K w ( s - h w ( t ) , f ( h w ( t ) ) ) d μ H ( t ) , w > 0, s ∈ G, where G and H are topological groups and h w w > 0 is a family of homeomorphisms h w : H h w ( H ) G . Such operators contain, in particular, a nonlinear version of the generalized sampling operators, which have many applications in the theory of signal processing.

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