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

Shiferaw Berhanu; Jorge Hounie

Displaying similar documents to “Traces and the F. and M. Riesz theorem for vector fields”

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...

Exponential decay of averaged Green functions for random Schrödinger operators. A direct approach

J. Sjöstrand, W.-M. Wang (1999)

Annales scientifiques de l'École Normale Supérieure

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Decay of Fourier transforms and summability of eigenfunction expansions

Luca Brandolini, Leonardo Colzani (2000)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Solvability near the characteristic set for a class of planar vector fields of infinite type

Alberto P. Bergamasco, Abdelhamid Meziani (2005)

Annales de l’institut Fourier

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We study the solvability of equations associated with a complex vector field $L$ in $ℝ^{2}$ with $C^{\infty}$ or $C^{ω}$ coefficients. We assume that $L$ is elliptic everywhere except on a simple and closed curve $Σ$ . We assume that, on $Σ$ , $L$ is of infinite type and that $L \land \bar{L}$ vanishes to a constant order. The equations considered are of the form $L u = p u + f$ , with $f$ satisfying compatibility conditions. We prove, in particular, that when the order of vanishing of $L \land \bar{L}$ is $> 1$ , the equation $L u = f$ is solvable in the $C^{\infty}$ category but not in the...