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Unitary holomorphic multiplier representations over a homogeneous bounded domain
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Hideyuki Ishi
Published/Copyright:
September 21, 2010
Abstract
We consider the unitarizability of multiplier representations of transformation groups defined on Hilbert spaces of holomorphic functions on a homogeneous bounded domain. In particular, for the Iwasawa subgroup of the holomorphic automorphism group the classification of the unitary multiplier representations is accomplished by making use of results in [Ishi, J. Funct. Anal. 167: 425–462, 1999]. As an application, the Wallach set of the homogeneous bounded domain is described.
Received: 2010-04-20
Accepted: 2010-05-31
Published Online: 2010-09-21
Published in Print: 2011-September
© de Gruyter 2011
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Articles in the same Issue
- Geometric and harmonic analysis on homogeneous spaces
- On the multiplicity formula of compact nilmanifolds with flat orbits
- Hilbert transform and related topics associated with Jacobi–Dunkl operators of compact and noncompact types
- Atomic decomposition of a real Hardy space for Jacobi analysis
- Unitary holomorphic multiplier representations over a homogeneous bounded domain
- A deformation approach of the Kirillov map for exponential groups
- Visible actions on the non-symmetric homogeneous space SO(8, ℂ)/G2(ℂ)
- A Paley–Wiener theorem for some eigenfunction expansions
- Estimate of the Lp-Fourier transform norm for connected nilpotent Lie groups
