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A Paley-Wiener Theorem for Selected Nilpotent Lie Groups

✍ Scribed by J.D. Moss

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
593 KB
Volume
114
Category
Article
ISSN
0022-1236

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✦ Synopsis

This paper concerns itself with the problem of generalizing to nilpotent Lie groups a weak form of the classical Paley-Wiener theorem for (\mathbb{R}^{n}). The generalization is accomplished for a large subclass of nilpotent Lie groups, as well as for an interesting example not in this subclass. The paper also shows that if (N) is any connected. simply connected nilpotent Lie group, then almost all representations (\pi) in the support of the Plancherel measure may be induced from a single family of Vergne polarizations, with each (\pi) being modelled in (L^{2}) of the same fixed subspace of the Lie algebra of N. ' 1993 Academic Press, Inc.

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