Lie Groups and Representation Theory

Seminar information archive ~07/20Next seminarFuture seminars 07/21~

Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.)

2006/07/25

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Boris Rubin (Louisiana State University)
Radon Transforms: Basic Concepts
[ Abstract ]
How can we reconstruct a function on a manifold from integrals of this function over certain submanifolds?
This is one of the central problems in integral geometry and tomography, which leads to the notion of the Radon transform.

The first talk is of introductory character.
We discuss basic ideas of the original Radon's paper (1917), then proceed to the Minkowski-Funk transform and more general totally geodesic Radon transforms on the $n$-dimensional unit sphere.
The main emphasis is an intimate connection of these transforms with the relevant harmonic analysis.
We will see that Radon transforms of this type and their inverses can be regarded as members of analytic families of suitable convolution operators and successfully studied in the framework of these families.

I also plan to discuss an open problem of small divisors on the unit sphere, which arises in studying injectivity of generalized Minkowski-Funk transforms for non-central spherical sections.
[ Reference URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html