Abstract
The restriction, from a compact Lie group K K to a closed subgroup, of a polynomially bounded representation remains polynomially bounded provided a geometric assumption on the asymptotic K K -support of the representation is satisfied. This is a theorem of T. Kobayashi. We give a proof of this theorem using microlocal analysis in the setting of distribution rather than hyperfunction theory. The proof is based on a characterization, up to the natural K × K K\times K action, of the wavefront set of a distribution on K K in terms of the asymptotic behavior of its Fourier coefficients.
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