Title: Injectivity of spherical means on $H$-type groups
Speaker: E.K. Narayanan (IISc Mathematics)
Date: 13 October 2021
Time: 4 pm
Venue: Microsoft Teams (online)
We consider three different spherical means on a Heisenberg type group.
First, the standard spherical means, which is the average of a function
over the spheres in the complement of the center of the group, second is
the average over product of spheres in the center and its complement and
the third one over spheres defined by a homogeneous norm on the group.
We establish injectivity results for these means on $L^p$ spaces for the
range $1 \leq p \leq 2m/(m-1)$ where $m$ is the dimension of the center.
Our results extend and generalize S. Thangavelu’s results for spherical
means on the Heisenberg group. (Joint work with P. K. Sanjay and K. T. Yasser)