# Approximation results for nonlinear integral operators in modular spaces and applications

Ilaria Mantellini; Gianluca Vinti

Annales Polonici Mathematici (2003)

- Volume: 81, Issue: 1, page 55-71
- ISSN: 0066-2216

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topIlaria 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 -

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