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

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      Permanent link:
      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 $s>0$ 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

       

      Rama Rawat1 R K Srivastava1

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

       
  • Proceedings – Mathematical Sciences | News

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