The spherical Paley-Wiener theorem on the complex Grassmann manifolds $\mbox {SU}(p+q)/\mbox {S}(\mbox {U}_p\times \mbox {U}_q)$
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- by Roberto Camporesi PDF
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Abstract:
We prove the Paley-Wiener theorem for the spherical transform on the complex Grassmann manifolds $U/K=\mbox {SU}(p+q)/\mbox {S}(\mbox {U}_p\times \mbox {U}_q)$. 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.References
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Additional Information
- Roberto Camporesi
- Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
- Email: camporesi@polito.it
- Received by editor(s): March 31, 2005
- Published electronically: March 22, 2006
- Communicated by: Dan M. Barbasch
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 2649-2659
- MSC (2000): Primary 43A85, 43A90; Secondary 33C50, 26A33
- DOI: https://doi.org/10.1090/S0002-9939-06-08408-5
- MathSciNet review: 2213744