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Displaying similar documents to “A theorem concerning the multipliers for functions with Fourier transforms in L p ”

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

María L. Torres de Squire (1993)

Publicacions Matemàtiques

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

A property of Fourier Stieltjes transforms on the discrete group of real numbers

Yngve Domar (1970)

Annales de l'institut Fourier

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Let μ be a Fourier-Stieltjes transform, defined on the discrete real line and such that the corresponding measure on the dual group vanishes on the set of characters, continuous on R . Then for every ϵ > 0 , { x ∈ R | Re ( μ ( x ) ) > ϵ } has a vanishing interior Lebesgue measure. If ϵ = 0 the statement is not generally true. The result is applied to prove a theorem of Rosenthal.