## Abstract The PaleyโWiener space __PW__ (__G__) on a stratified Lie group __G__ is defined via the spectral decomposition of the associated subโLaplacian. In this paper, we show that functions in __PW__ (โ), where โ denotes the Heisenberg group, extend to an entire function on the complexificatio
On Paley-Wiener Theorems for the Heisenberg Group
โ Scribed by S. Thangavelu
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 576 KB
- Volume
- 115
- Category
- Article
- ISSN
- 0022-1236
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๐ SIMILAR VOLUMES
We prove a topological Paley Wiener theorem for the Fourier transform defined on the real hyperbolic spaces SO o ( p, q)รSO o ( p&1, q), for p, q # 2N, without restriction to K-types. We also obtain Paley Wiener type theorems for L \_ -Schwartz functions (0<\_ 2) for fixed K-types.
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. T
E. Damek, A. Hulanicki, and R. Penney (J. Funct. Anal., in press) studied a canonical system of differential equations (the Hua system) denoted HJK which is definable on any Ka hlerian manifold M. Functions annihilated by this system are called ``Hua-harmonic.'' In the case where M is a bounded homo