• Rama Rawat

      Articles written in Proceedings – Mathematical Sciences

    • A theorem of the Wiener—Tauberian type forL1(Hn)

      Rama Rawat

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      The Heisenberg motion groupHM(n), which is a semi-direct product of the Heisenberg group Hn and the unitary group U(n), acts on Hn in a natural way. Here we prove a Wiener-Tauberian theorem for L1 (Hn) with this HM(n)-action on Hn i.e. we give conditions on the “group theoretic” Fourier transform of a functionf in L1 (Hn) in order that the linear span ofgf : g∈HM(n) is dense in L1(Hn), wheregf(z, t) =f(g·(z, t)), forg ∈ HM(n), (z,t)∈Hn.

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

      Rama Rawat R K Srivastava

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      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.

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