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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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Harish-Chandra’s Plancherel theorem for $\frak p$-adic groups
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by Allan J. Silberger PDF
Trans. Amer. Math. Soc. 348 (1996), 4673-4686 Request permission

Erratum: Trans. Amer. Math. Soc. 352 (2000), 1947-1949.

Abstract:

Let $G$ be a reductive $\mathfrak {p}$-adic group. In his paper, “The Plancherel Formula for Reductive $\mathfrak {p}$-adic Groups", Harish-Chandra summarized the theory underlying the Plancherel formula for $G$ and sketched a proof of the Plancherel theorem for $G$. One step in the proof, stated as Theorem 11 in Harish-Chandra’s paper, has seemed an elusively difficult step for the reader to supply. In this paper we prove the Plancherel theorem, essentially, by proving a special case of Theorem 11. We close by deriving a version of Theorem 11 from the Plancherel theorem.
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Additional Information
  • Allan J. Silberger
  • Affiliation: Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115
  • Email: silberger@math.csuohio.edu
  • Received by editor(s): July 6, 1995
  • Received by editor(s) in revised form: December 15, 1995
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 4673-4686
  • MSC (1991): Primary 22E50
  • DOI: https://doi.org/10.1090/S0002-9947-96-01700-X
  • MathSciNet review: 1370652