Compact Courses
Spherical Radon transform: new problems and applications
by
Prof. Mark Agranovsky
Bar-Ilan University, Israel
September 11 - 25, 2008
(on all Mondays, Wednesdays & Thursdays starting on Thursday)
at
L H – 1, Department of Mathematics
Indian Institute of Science, Bangalore
Abstract
This series of lecture will be devoted to survey of recent results in integral geometry on spheres. The central object here is the spherical mean operator - the classical transform playing an important role in analysis and differential equations.
The new interest to this old object arose in mid 90’s due to new circle of problems: on one side, in pure mathematics, namely, in approximation theory (characterizing complete systems of spherical waves), PDE (describing nodal sets for the wave equation) and, on the other side (and surprisingly almost at the same time) in applications, namely in thermo- and photoacoustic tomography - new technologies in medical imaging.
In the above theoretical and practical applications, one views spherical means as a Radon type transform defined on non-standard complexes of spheres. Main questions of integral geometry and mathematical tomography-injectivity, range description and inversion, applying to this transform, lead to interesting and challenging mathematical problems which were little studied by recently. We will describe the progress in study of the subject in the past decade or so and discuss questions which still remain open
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