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A Paley-Wiener Theorem for All Two- and Three-Step Nilpotent Lie Groups

✍ Scribed by R. Park

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 918 KB
Volume: 133
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1995.1126

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✦ Synopsis

A Paley-Wiener theorem for all connected, simply-connected two- and three-step nilpotent Lie groups is proved. If (f \in L_{i}^{x}(G)), where (G) is a connected, simplyconnected two- or three-step nilpotent Lie group such that the operator-valued Fourier transform (\hat{\varphi}(\pi)=0) for all (\pi) in (E), a subset of (\hat{G}) of positive Plancherel measure, then it is shown that (f=0) a.e. on (G). The proof uses representationtheoretic methods from Kirillov theory for nilpotent Lie groups and an integral formula for the operator-valued Fourier transform (\hat{\varphi}(\pi)). 1995 Academic Press, Inc.

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