Välkommen till en dubbel föreläsning i seminarieserien i matematik.
Föreläsare/Lecturer 1, at 13.15-14.00
Jan Boman, professor emeritus, Stockholms universitet
Radon transforms supported in hypersurfaces and a conjecture by Arnold
A famous lemma in Newton's Principia says that the area of a segment of a bounded convex domain in the plane cannot depend algebraically on the parameters of the line that denes the segment. Vassiliev extended Newton's lemma to bounded domains in arbitrary even dimensions. In odd dimensions the volume cut out from an ellipsoid by a hyperplane depends not only algebraically but polynomially on the position of the hyperplane. Arnold conjectured in 1987 that ellipsoids in odd dimensions are the only cases in which the volume function in question is algebraic.
The special case when the volume function is assumed to be polynomial has been studied in several papers and was settled very recently. Motivated by a problem concerning the so-called interior Radon transform I recently tried to construct a compactly supported distribution f ≠ 0 whose Radon transform is supported in the set of tangent planes to the boundary surface δD of a bounded convex domain D ⊂ ℝn. However, I found that such distributions can exist only if δD is an ellipsoid. This result gives a new proof of the abovementioned special case of Arnold's conjecture.
Föreläsare/Lecturer 2, at 14.15-15.00
Habib Ouerdiane, professor, Université de Tunis El Manar, Tunisien
Solutions of infinite dimensional evolution equations
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