Institute of Mathematics for Industry

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Integral geometry, mean value theorems, and wave equations


Hold Date 2012-06-25 16:00~2012-06-25 17:00

Place Seminar Room 3, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Fulton Gonzalez (Tufts University)

Abstract:
This talk introduces various methods of solving wave equations
in the Euclidean and symmetric space settings. The methods include
the use of Fourier transforms, Radon transforms, and mean value
theorems. In the symmetric space setting, we focus on a
"multitemporal system" introduced by Semenov-Tjan-Shansky and
its relation to the horocycle Radon transform. We also present
mean value solutions which employ the hypergeometric shift
operators of Heckman and Opdam. These solutions generalize
some results on rank one symmetric spaces obtained by Lax-Phillips
and by Helgason.