Gegenbauer-Chebyshev Integrals and Radon Transforms

יום ב', 04/05/2015 - 14:00
The Radon transform $R$ assigns to a function $f$ on $R^n$  a collection 
of integrals of that function over   hyperplanes in $R^n$. Suppose 
that $Rf$ vanishes on  all hyperplanes that do not meet a fixed convex 
set. {\it Does it follow that $f$ is zero in the exterior of that set?}
I am planning to discuss new results related to this question and  the
corresponding injectivity problems. If time allows, some   projectively
equivalent modifications of $R$ will be considered.