Approximation results for nonlinear integral operators in modular spaces and applications

Ilaria Mantellini, and Gianluca Vinti. "Approximation results for nonlinear integral operators in modular spaces and applications." Annales Polonici Mathematici 81.1 (2003): 55-71. <http://eudml.org/doc/280206>.

@article{IlariaMantellini2003,
abstract = {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.},
author = {Ilaria Mantellini, Gianluca Vinti},
journal = {Annales Polonici Mathematici},
keywords = {nonlinear integral operators; modular convergence; nonlinear generalized sampling series},
language = {eng},
number = {1},
pages = {55-71},
title = {Approximation results for nonlinear integral operators in modular spaces and applications},
url = {http://eudml.org/doc/280206},
volume = {81},
year = {2003},
}

TY - JOUR
AU - Ilaria Mantellini
AU - Gianluca Vinti
TI - Approximation results for nonlinear integral operators in modular spaces and applications
JO - Annales Polonici Mathematici
PY - 2003
VL - 81
IS - 1
SP - 55
EP - 71
AB - 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.
LA - eng
KW - nonlinear integral operators; modular convergence; nonlinear generalized sampling series
UR - http://eudml.org/doc/280206
ER -