A Paley-Wiener theorem for locally compact Abelian groups

  title={A Paley-Wiener theorem for locally compact Abelian groups},
  author={Gunar E. Liepins},
  journal={Transactions of the American Mathematical Society},
  • G. Liepins
  • Published 1 September 1976
  • Mathematics
  • Transactions of the American Mathematical Society
Extending the Paley-Wiener theorem to locally compact Abelian groups involves both finding a suitable Laplace transform and a suitable analogue for analytic functions. The Laplace transform is defined in terms of complex-characters, and differentiability is defined with use of one-parameter subgroups. The resulting theorem is much as conjectured by Mackey [71,(1) the major differences being that the theorem is very much an L2 theorem and that the problem exhibits a surprising finite dimensional… 

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