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Displaying similar documents to “Decay of Fourier transforms and summability of eigenfunction expansions”

On summability of measures with thin spectra

Maria Roginskaya, Michaël Wojciechowski (2004)

Annales de l’institut Fourier

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We study different conditions on the set of roots of the Fourier transform of a measure on the Euclidean space, which yield that the measure is absolutely continuous with respect to the Lebesgue measure. We construct a monotone sequence in the real line with this property. We construct a closed subset of d which contains a lot of lines of some fixed direction, with the property that every measure with spectrum contained in this set is absolutely continuous. We also give examples of sets...