Pointwise convergence of the Fourier transform on locally compact abelian groups.

Torres de Squire, María L.. "Pointwise convergence of the Fourier transform on locally compact abelian groups.." Publicacions Matemàtiques 37.1 (1993): 45-55. <http://eudml.org/doc/41524>.

@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 -