Pointwise convergence of the Fourier transform on locally compact abelian groups

• Autores: María L. Torres de Squire
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 37, Nº 1, 1993, págs. 45-55
• Idioma: inglés
• DOI: 10.5565/publmat_37193_03
• Títulos paralelos:
  • Convergencia puntual de la transformada de Fourier en grupos abelianos localmente compactos
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• Resumen

  • We extend to locally compact abelian groups, Fejer's theorem on pointwise convergence of the Fourier transform. We prove that lim fU * f(y) = f (y) almost everywhere for any function f in the space (LP, l8)(G) (hence in LP(G)), 2 = p = 8, where {fU} 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.