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Local injectivity for generalized Radon transforms

Presented by: 
J Boman
Date: 
Thursday 27th October 2011 - 14:00 to 15:00
Venue: 
INI Seminar Room 2
Abstract: 
For a given smooth, positive function $m(x, \xi, \eta)$ we consider a weighted Radon transform $R$ defined by $Rf(\xi, \eta) = \int f(x, \xi x + \eta) m(\xi, \eta, x) dx$ for functions $f(x, y)$ that are defined in some neighborhood of the origin and are supported in $y\ge x^2$. The question is for which $m(x, \xi, \eta)$ it is true that $R$ is injective. A similar problem when the family of lines $y = \xi x + \eta$ is replaced by a family of curves is also considered.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons