Approximation results for nonlinear integral operators in modular spaces and applications

Ilaria Mantellini; Gianluca Vinti

Annales Polonici Mathematici, Tome 81 (2003), p. 55-71 / Harvested from The Polish Digital Mathematics Library

Résumé

We obtain modular convergence theorems in modular spaces for nets of operators of the form $(T_{w} f) (s) = \int_{H} K_{w} (s - h_{w} (t), f (h_{w} (t))) d μ_{H} (t)$ , w > 0, s ∈ G, where G and H are topological groups and ${h_{w}}_{w > 0}$ is a family of homeomorphisms $h_{w} : H \to h_{w} (H) \subset G .$ Such operators contain, in particular, a nonlinear version of the generalized sampling operators, which have many applications in the theory of signal processing.

Publié le : 2003-01-01

Zbl 1019.41013

EUDML-ID : urn:eudml:doc:280206

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     title = {Approximation results for nonlinear integral operators in modular spaces and applications},
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     year = {2003},
     pages = {55-71},
     zbl = {1019.41013},
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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) pp. 55-71. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap81-1-5/