Comptes Rendus
no. 23-24
Mathematical Analysis
Flatness of distributions vanishing on infinitely many hyperplanes
Jean-Michel Bony
Jan Boman1
1Department of Mathematics, Stockholm University, SE 10691, Stockholm, Sweden
Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1351-1354

Let {Lk}k=1∞ be a family of hyperplanes in Rn and let L0 be a limiting hyperplane of {Lk}. Let u be a distribution that satisfies a natural wave front condition and has vanishing restrictions to Lk for all k⩾1. Then u must be flat at L0.

Soit {Lk}k=1∞ une famille d'hyperplans dans Rn et soit L0 un hyperplan limite de {Lk}. Si u est une distribution satisfaisant à une condition naturelle portant sur le front d'onde et qui s'annule sur Lk pour tout k⩾1, alors u est plate sur L0.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.10.028

Jan Boman  1

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

[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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