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

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/106/04/0369-0377

    • Keywords

       

      Heisenberg group; Gelfand pairs; class-1 representations; elementary spherical functions

    • Abstract

       

      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.

    • Author Affiliations

       

      Rama Rawat1

      1. Statistics and Mathematics Unit, Indian Statistical Institute, R. V. College Post, Bangalore - 560059, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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