Geodesic
Fourier Transforms of Unbounded Measures
Canadian journal of mathematics, Tome 31 (1979) no. 6, pp. 1281-1292

Voir la notice de l'article provenant de la source Cambridge University Press

1. Introduction. One of the basic objects of study in harmonic analysis is the Fourier transform (or Fourier-Stieltjes transform) μ of a bounded (complex) measure μ on the real line R: (1.1) More generally, if μ is a bounded measure on a locally compact abelian group G, then its Fourier transform is the function (1.2) where Ĝ is the dual group of G and One answer to the question “Which functions can be represented as Fourier transforms of bounded measures?” was given by the following criterion due to Schoenberg [11] for the real line and Eberlein [5] in general: f is a Fourier transform of a bounded measure if and only if there is a constant M such that (1.3) for all φ ∈ L1(G) where 
Stewart, James. Fourier Transforms of Unbounded Measures. Canadian journal of mathematics, Tome 31 (1979) no. 6, pp. 1281-1292. doi: 10.4153/CJM-1979-106-4
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