Radon Transforms over Horospheres in Real Hyperbolic Space
Seminar
Speaker
Prof. Boris Rubin, Louisiana State University, USA
Date
10/12/2018 - 15:00 - 14:00Add to Calendar
2018-12-10 14:00:00
2018-12-10 15:00:00
Radon Transforms over Horospheres in Real Hyperbolic Space
The horospherical Radon transform integrates functions on the n-dimensional real
hyperbolic space over d-dimensional horospheres, where d is a fixed integer, $1\le d\le n-1$.
Using the tools of real analysis, we obtain sharp existence conditions and explicit inversion
formulas for these transforms acting on smooth functions and functions belonging to $L^p$. The
case d = n-1 agrees with the classical Gelfand-Graev transform which was studied before in
terms of the distribution theory on rapidly decreasing smooth functions. The results for
$L^p$-functions and the case d < n-1 are new. This is a joint work with William O. Bray.
2nd floor Colloquium Room, Building 216
אוניברסיטת בר-אילן - Department of Mathematics
mathoffice@math.biu.ac.il
Asia/Jerusalem
public
Place
2nd floor Colloquium Room, Building 216
Abstract
The horospherical Radon transform integrates functions on the n-dimensional real
hyperbolic space over d-dimensional horospheres, where d is a fixed integer, $1\le d\le n-1$.
Using the tools of real analysis, we obtain sharp existence conditions and explicit inversion
formulas for these transforms acting on smooth functions and functions belonging to $L^p$. The
case d = n-1 agrees with the classical Gelfand-Graev transform which was studied before in
terms of the distribution theory on rapidly decreasing smooth functions. The results for
$L^p$-functions and the case d < n-1 are new. This is a joint work with William O. Bray.
Last Updated Date : 09/12/2018
