Approximation results for nonlinear integral operators in modular spaces and applications

• Autorzy: Ilaria Mantellini , Gianluca Vinti
• Języki publikacji: EN

Abstrakty

EN

We obtain modular convergence theorems in modular spaces for nets of operators of the form $(T_wf)(s) = ∫_{H} K_w (s - h_w(t),f(h_w(t))) dμ_H(t)$, 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.

Kategorie tematyczne

• 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytski{\u\i}, Uryson, etc.)
• 47G10: Integral operators
• 46A80: Modular spaces
• 41A35: Approximation by operators (in particular, by integral operators)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2003
• Tom: 81
• Numer: 1
• Strony: 55-71

Daty

wydano

2003

Twórcy

autor

Ilaria Mantellini

• Department of Mathematics and Informatics, University of Perugia, Via Vanvitelli 1, 06123 Perugia, Italy

autor

Gianluca Vinti

• Department of Mathematics and Informatics, University of Perugia, Via Vanvitelli 1, 06123 Perugia, Italy

Identyfikatory

DOI

10.4064/ap81-1-5