Fourier series on compact Lie groups

  title={Fourier series on compact Lie groups},
  author={Michael E. Taylor},
In [I], Gong Shang proves that the Fourier series of a sufficiently smooth function on a unitary group U(n) converges absolutely and uniformly. Using the theory of elliptic operators, we give a short proof of a more general assertion. Suppose m is a finite strictly positive measure on a compact Cmanifold M. Suppose L is a strictly elliptic operator of order k on M which is selfadjoint on the space L2(M) of square integrable functions with respect to m. Then it is well known that for a… CONTINUE READING