Displaying similar documents to “Sidon sets and Riesz sets for some measure algebras on the disk”

A microlocal F. and M. Riesz theorem with applications.

Raymondus G. M. Brummelhuis (1989)

Revista Matemática Iberoamericana

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Consider, by way of example, the following F. and M. Riesz theorem for R: Let μ be a finite measure on R whose Fourier transform μ* is supported in a closed convex cone which is proper, that is, which contains no entire line. Then μ is absolutely continuous (cf. Stein and Weiss [SW]). Here, as in the sequel, absolutely continuous means with respect to Lebesque measure. In this theorem one can replace the condition on the support of μ* by a similar condition on the wave front set WF(μ)...

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 ℝ 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...