• Spherical Means in Annular Regions in the 𝑛-Dimensional Real Hyperbolic Spaces

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/121/03/0311-0325

• # Keywords

Real hyperbolic spaces; spherical means; spherical harmonics.

• # Abstract

Let $Z_{r,R}$ be the class of all continuous functions 𝑓 on the annulus $\mathrm{Ann}(r,R)$ in the real hyperbolic space $\mathbb{B}^n$ with spherical means $M_sf(x)=0$, whenever $s&gt;0$ and $x\in\mathbb{B}^n$ are such that the sphere $S_s(x)\subset\mathrm{Ann}(r,R)$ and $B_r(o)\subseteq B_s(x)$. In this article, we give a characterization for functions in $Z_{r,R}$. In the case $R=\infty$, this result gives a new proof of Helgason’s support theorem for spherical means in the real hyperbolic spaces.

• # Author Affiliations

1. Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208 016, India

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019