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

Raymondus G. M. Brummelhuis

Displaying similar documents to “A microlocal F. and M. Riesz theorem with applications.”

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...

On the theorem of F. and M. Riesz

Louis Pigno, Sadahiro Saeki (1990)

Colloquium Mathematicae

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Henkin measures, Riesz products and singular sets

Evgueni Doubtsov (1998)

Annales de l'institut Fourier

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The mutual singularity problem for measures with restrictions on the spectrum is studied. The $d$ -pluriharmonic Riesz product construction on the complex sphere is introduced. Singular pluriharmonic measures supported by sets of maximal Hausdorff dimension are obtained.

Riesz means of Fourier transforms and Fourier series on Hardy spaces

Ferenc Weisz (1998)

Studia Mathematica

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Elementary estimates for the Riesz kernel and for its derivative are given. Using these we show that the maximal operator of the Riesz means of a tempered distribution is bounded from $H_{p} (ℝ)$ to $L_{p} (ℝ)$ (1/(α+1) < p < ∞) and is of weak type (1,1), where $H_{p} (ℝ)$ is the classical Hardy space. As a consequence we deduce that the Riesz means of a function $⨍ \in L_{1} (ℝ)$ converge a.e. to ⨍. Moreover, we prove that the Riesz means are uniformly bounded on $H_{p} (ℝ)$ whenever 1/(α+1) < p < ∞. Thus, in case $⨍ \in H_{p} (ℝ)$ , the Riesz...

The linear modulus of an integral operator

A. C. Zaanen (1972)

Mémoires de la Société Mathématique de France

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Some remarks on Bochner-Riesz means

S. Thangavelu (2000)

Colloquium Mathematicae

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We study $L^{p}$ norm convergence of Bochner-Riesz means $S_{R}^{δ} f$ associated with certain non-negative differential operators. When the kernel $S_{R}^{m} (x, y)$ satisfies a weak estimate for large values of m we prove $L^{p}$ norm convergence of $S_{R}^{δ} f$ for δ > n|1/p-1/2|, 1 < p < ∞, where n is the dimension of the underlying manifold.

Remark On Fatou-Riesz's Theorem

Vojislav G. Avakumović (1955)

Publications de l'Institut Mathématique

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Traces and the F. and M. Riesz theorem for vector fields

Shiferaw Berhanu, Jorge Hounie (2003)

Annales de l’institut Fourier

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This work studies conditions that insure the existence of weak boundary values for solutions of a complex, planar, smooth vector field $L$ . Applications to the F. and M. Riesz property for vector fields are discussed.