A theorem on the Schwartz space of a reductive Lie group.

  title={A theorem on the Schwartz space of a reductive Lie group.},
  author={James Arthur},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  volume={72 12},
  • James Arthur
  • Published 1975 in
    Proceedings of the National Academy of Sciences…
The purpose of this paper is to define the Fourier transform of an arbitrary tempered distribution on a reductive Lie group. To this end we define a topological vector space, [unk](G), in terms of the classes of irreducible unitary representations of G, which plays role of a dual Schwartz space. Our main theorem then asserts that the usual L(2) Fourier transform, when restricted to functions in the Schwartz space, [unk](G) defined by Harish-Chandra, provides a topological isomorphism from [unk… CONTINUE READING

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