Unique continuation of microlocally analytic distributions and injectivity theorems for the ray transform

• Using a vanishing theorem for microlocally real analytic distributions and a theorem on flatness of a distribution vanishing on infinitely many hyperplanes we give a new proof of an injectivity theorem of Bélisle, Massé, and Ransford for the ray transform on R^n. By means of  an example we show  that this result is sharp. An extension is given where real analyticity is replaced by quasianalyticity.

Ämnesord

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

ray transform

analytic wave front set

Mathematical analysis

Analys

Mathematics

matematik

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