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A question about bdd operator T on L2(G)

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  • Ali akbar Arefijamaal
    Hi, Let $G$ be a LC group and $T:L^{2}(G) longrightarrow L^{2}(G)$ be a bdd operator. Also assume that $ alpha in Aut(G)$. I think that
    Message 1 of 3 , Jun 11, 2007
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      Hi,
      Let $G$ be a LC group and $T:L^{2}(G)\longrightarrow L^{2}(G)$ be
      a bdd operator. Also assume that $\alpha\in Aut(G)$. I think that
      $$T(f\circ\alpha)=T(f)\circ\alpha.$$
      But I Cann't proof or disproof it. Even a reference to the proof
      will help. Thanks


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    • Hendra Gunawan
      Dear Colleagues, If one can interpret the Laplacian $ Delta$ as curvature or strain energy, is there a geometric or physical interpretation of $ Delta^{3/2}$??
      Message 2 of 3 , Sep 17, 2007
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        Dear Colleagues,

        If one can interpret the Laplacian $\Delta$ as curvature or
        strain energy, is there a geometric or physical interpretation
        of $\Delta^{3/2}$??

        Hendra Gunawan
      • Hendra Gunawan
        I am sorry, but what I am interested in is actually $ Delta^{3/4}$. Hendra Gunawan
        Message 3 of 3 , Sep 17, 2007
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          I am sorry, but what I am interested in is actually $\Delta^{3/4}$.

          Hendra Gunawan

          > Dear Colleagues,
          >
          > If one can interpret the Laplacian $\Delta$ as curvature or
          > strain energy, is there a geometric or physical interpretation
          > of $\Delta^{3/2}$??
          >
          > Hendra Gunawan
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