Displaying similar documents to “Henkin measures, Riesz products and singular sets”

On Riesz product measures ; mutual absolute continuity and singularity

Shelby J. Kilmer, Sadahiro Saeki (1988)

Annales de l'institut Fourier

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We give some criteria for mutual absolute continuity and for singularity of Riesz product measures on locally compact abelian groups. The first section gives the definition of such a measure which is more general than the usual definition. The second section provides three sufficient conditions for one Riesz product measure to be absolutely continuous with respect to another. One of our results contains a theorem of Brown-Moran-Ritter as a special case. The final section deals with random...

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...

Singular measures and the key of G.

Stephen M. Buckley, Paul MacManus (2000)

Publicacions Matemàtiques

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We construct a sequence of doubling measures, whose doubling constants tend to 1, all for which kill a G set of full Lebesgue measure.

The higher order Riesz transform for Gaussian measure need not be of weak type (1,1)

Liliana Forzani, Roberto Scotto (1998)

Studia Mathematica

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The purpose of this paper is to prove that the higher order Riesz transform for Gaussian measure associated with the Ornstein-Uhlenbeck differential operator L : = d 2 / d x 2 - 2 x d / d x , x ∈ ℝ, need not be of weak type (1,1). A function in L 1 ( d γ ) , where dγ is the Gaussian measure, is given such that the distribution function of the higher order Riesz transform decays more slowly than C/λ.