Resumen de Pointwise convergence of the Fourier transform on locally compact abelian groups

María L. Torres de Squire

• 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.