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The spherical Paley-Wiener theorem on the complex Grassmann manifolds SU$ (p+q)/$S$ ($U$ _p\times$   U$ _q)$

Author: Roberto Camporesi
Journal: Proc. Amer. Math. Soc. 134 (2006), 2649-2659
MSC (2000): Primary 43A85, 43A90; Secondary 33C50, 26A33
Published electronically: March 22, 2006
MathSciNet review: 2213744
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Abstract: We prove the Paley-Wiener theorem for the spherical transform on the complex Grassmann manifolds $ U/K=$SU$ (p+q)/$S$ ($U$ _p\times$   U$ _q)$. This theorem characterizes the $ K$-biinvariant smooth functions $ f$ on the group $ U$ that are supported in the $ K$-invariant ball of radius $ R$, with $ R$ less than the injectivity radius of $ U/K$, in terms of holomorphic extendability, exponential growth, and Weyl invariance properties of the spherical Fourier transforms $ \hat{f}$, originally defined on the discrete set $ \Lambda_{sph}$ of highest restricted spherical weights.

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Additional Information

Roberto Camporesi
Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Keywords: Symmetric spaces, representation theory, Paley-Wiener theorems
Received by editor(s): March 31, 2005
Published electronically: March 22, 2006
Communicated by: Dan M. Barbasch
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.