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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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A Paley-Wiener theorem for locally compact abelian groups
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by Gunar E. Liepins PDF
Trans. Amer. Math. Soc. 222 (1976), 193-210 Request permission


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 [7],($^{1}$) the major differences being that the theorem is very much an ${L^2}$ theorem and that the problem exhibits a surprising finite dimensional nature.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 222 (1976), 193-210
  • MSC: Primary 43A32
  • DOI:
  • MathSciNet review: 0430679