[02369] Unique continuation results for generalized ray transforms
Session Time & Room : 3C (Aug.23, 13:20-15:00) @F311
Type : Contributed Talk
Abstract : We discuss unique continuation results for certain generalized ray transforms. We prove that if the generalized ray transform of a function vanishes along all lines passing through an open set in Euclidean space, and the function vanishes in that same open set, then the function vanishes identically. We give an example to show that the second assumption cannot be removed. We also consider generalized transforms on higher order objects such as vector fields, symmetric 2-tensor fields etc., and under the same hypotheses, show that a certain component vanishes. Since such ray transforms have a non-trivial kernel, this is the optimal result that one can expect.
