Flatness of distributions vanishing on infinitely many hyperplanes

Jan Boman

doi:10.1016/j.crma.2009.10.028

Mathematical Analysis

Flatness of distributions vanishing on infinitely many hyperplanes
[Platitude des distributions s'annulant sur une infinité d'hyperplans]

Présenté par : Jean-Michel Bony

Jan Boman ¹

¹ Department of Mathematics, Stockholm University, SE 10691, Stockholm, Sweden

Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1351-1354.

Résumé
Abstract

Soit ${L_{k}}_{k = 1}^{\infty}$ une famille d'hyperplans dans $R^{n}$ et soit $L_{0}$ un hyperplan limite de ${L_{k}}$ . Si u est une distribution satisfaisant à une condition naturelle portant sur le front d'onde et qui s'annule sur $L_{k}$ pour tout $k ⩾ 1$ , alors u est plate sur $L_{0}$ .

Let ${L_{k}}_{k = 1}^{\infty}$ be a family of hyperplanes in $R^{n}$ and let $L_{0}$ be a limiting hyperplane of ${L_{k}}$ . Let u be a distribution that satisfies a natural wave front condition and has vanishing restrictions to $L_{k}$ for all $k ⩾ 1$ . Then u must be flat at $L_{0}$ .

Reçu le : 2009-04-07
Accepté le : 2009-10-28
Publié le : 2009-11-10

DOI : 10.1016/j.crma.2009.10.028

Affiliations des auteurs :

Jan Boman ¹

¹ Department of Mathematics, Stockholm University, SE 10691, Stockholm, Sweden

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     author = {Jan Boman},
     title = {Flatness of distributions vanishing on infinitely many hyperplanes},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1351--1354},
     publisher = {Elsevier},
     volume = {347},
     number = {23-24},
     year = {2009},
     doi = {10.1016/j.crma.2009.10.028},
     language = {en},
}

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Jan Boman. Flatness of distributions vanishing on infinitely many hyperplanes. Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1351-1354. doi : 10.1016/j.crma.2009.10.028. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.10.028/

Bibliographie
Cité par

[1] C. Béslisle; J.-C. Massé; T. Ransford When is a probability measure determined by infinitely many projections?, Ann. Probab., Volume 25 (1997), pp. 767-786

[2] J. Boman A local vanishing theorem for distributions, C. R. Acad. Sci. Paris, Ser. I, Volume 315 (1992), pp. 1231-1234

[3] J. Boman, Unique continuation of microlocally analytic distributions and injectivity theorems for the ray transform, Inverse Probl. Imaging, in press

[4] L. Hörmander The Analysis of Linear Partial Differential Operators, vol. 1, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983

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