# A Paley-Wiener theorem for locally compact Abelian groups

@article{Liepins1976APT, title={A Paley-Wiener theorem for locally compact Abelian groups}, author={Gunar E. Liepins}, journal={Transactions of the American Mathematical Society}, year={1976}, volume={222}, pages={193-210} }

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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