# Mathematical Sciences Research Institute

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# Seminar

Local and Global Injectivity for Weighted Radon Transforms" October 29, 2010
Parent Program: -- MSRI: Baker Board Room
Speaker(s) Jan Boman
Description Location: Bakerboard Room

Abstract:
The local injectivity problem for a weighted plane Radon transform can be formulated as follows. Let there be given a smooth, positive function $m(x, \xi, \eta)$ defined in a neighborhood of the origin in $\bold R3$. We want to know if it is true that \begin{align*} & f(x, y) = 0 \quad \textrm{for $y < x2$ \quad and} \\  \int f(x, \xi x + \eta) & m(x, \xi, \eta) dx = 0 \quad \textrm{for $(\xi, \eta)$ in some neighborhood of the origin} \end{align*} implies \begin{equation*} f(x,y) = 0 \quad \textrm{in some neighborhood of the origin.} \end{equation*}
I will discuss some old and new results on this problem as well as related
results for the corresponding global problem.
Video