@article{TorresdeSquire1993,
abstract = {We extend to locally compact abelian groups, Fejer's theorem on pointwise convergence of the Fourier transform. We prove that lim φU * f(y) = f (y) almost everywhere for any function f in the space (LP, l∞)(G) (hence in LP(G)), 2 ≤ p ≤ ∞, where \{φU\} is Simon's generalization to locally compact abelian groups of the summability Fejer Kernel. Using this result, we extend to locally compact abelian groups a theorem of F. Holland on the Fourier transform of unbounded measures of type q.},
author = {Torres de Squire, María L.},
journal = {Publicacions Matemàtiques},
keywords = {Análisis armónico abstracto; Grupos abelianos; Transformada de Fourier; Convergencia puntual; locally compact abelian groups; Fejér’s theorem; Fourier transform; summability Fejér kernel},
language = {eng},
number = {1},
pages = {45-55},
title = {Pointwise convergence of the Fourier transform on locally compact abelian groups.},
url = {http://eudml.org/doc/41524},
volume = {37},
year = {1993},
}
TY - JOUR
AU - Torres de Squire, María L.
TI - Pointwise convergence of the Fourier transform on locally compact abelian groups.
JO - Publicacions Matemàtiques
PY - 1993
VL - 37
IS - 1
SP - 45
EP - 55
AB - We extend to locally compact abelian groups, Fejer's theorem on pointwise convergence of the Fourier transform. We prove that lim φU * f(y) = f (y) almost everywhere for any function f in the space (LP, l∞)(G) (hence in LP(G)), 2 ≤ p ≤ ∞, where {φU} is Simon's generalization to locally compact abelian groups of the summability Fejer Kernel. Using this result, we extend to locally compact abelian groups a theorem of F. Holland on the Fourier transform of unbounded measures of type q.
LA - eng
KW - Análisis armónico abstracto; Grupos abelianos; Transformada de Fourier; Convergencia puntual; locally compact abelian groups; Fejér’s theorem; Fourier transform; summability Fejér kernel
UR - http://eudml.org/doc/41524
ER -
