Displaying similar documents to “Recent developments on the F. and M. Riesz theorem”

Sidon sets and Riesz sets for some measure algebras on the disk

Olivier Gebuhrer, Alan Schwartz (1997)

Colloquium Mathematicae

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Sidon sets for the disk polynomial measure algebra (the continuous disk polynomial hypergroup) are described completely in terms of classical Sidon sets for the circle; an analogue of the F. and M. Riesz theorem is also proved.

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...

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)...