The behavior of Fourier transforms for nilpotent Lie groups
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- by Ronald L. Lipsman and Jonathan Rosenberg PDF
- Trans. Amer. Math. Soc. 348 (1996), 1031-1050 Request permission
Abstract:
We study weak analogues of the Paley-Wiener Theorem for both the scalar-valued and the operator-valued Fourier transforms on a nilpotent Lie group $G$. Such theorems should assert that the appropriate Fourier transform of a function or distribution of compact support on $G$ extends to be “holomorphic” on an appropriate complexification of (a part of) $\hat G$. We prove the weak scalar-valued Paley-Wiener Theorem for some nilpotent Lie groups but show that it is false in general. We also prove a weak operator-valued Paley-Wiener Theorem for arbitrary nilpotent Lie groups, which in turn establishes the truth of a conjecture of Moss. Finally, we prove a conjecture about Dixmier-Douady invariants of continuous-trace subquotients of $C^{*}(G)$ when $G$ is two-step nilpotent.References
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Additional Information
- Ronald L. Lipsman
- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- Email: rll@math.umd.edu
- Jonathan Rosenberg
- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- MR Author ID: 298722
- ORCID: 0000-0002-1531-6572
- Email: jmr@math.umd.edu
- Received by editor(s): September 4, 1994
- Additional Notes: Both authors were partially supported by NSF grant DMS-92-25063.
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 348 (1996), 1031-1050
- MSC (1991): Primary 22E27; Secondary 43A30, 44A12, 22D25
- DOI: https://doi.org/10.1090/S0002-9947-96-01583-8
- MathSciNet review: 1370646