Equipartition of Energy for Waves in Symmetric Space

  title={Equipartition of Energy for Waves in Symmetric Space},
  author={Thomas P. Branson},
Let X = G=K be an odd-dimensional semisimple Riemannian symmetric space of the noncompact type, and suppose that all Cartan subgroups of G are conjugate. Let u be a real-valued classical solution of the modiied wave equation u tt = ((+ k)u on R X, the Cauchy data of which are supported in a closed metric ball of radius a at time t = 0. Here t is the coordinate on R, is the (nonpositive deenite) Laplace-Beltrami operator on X, and k is a positive constant depending on the root structure of the… CONTINUE READING

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