Hua operators, Poisson transform and relative discrete series on line bundle over bounded symmetric domains

Khalid Koufany; Genkai Zhang

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arXiv · 1105.3806

Hua operators, Poisson transform and relative discrete series on line bundle over bounded symmetric domains

Khalid Koufany·Genkai Zhang

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Abstract

Let $Ω=G/K$ be a bounded symmetric domain and $S=K/L$ its Shilov boundary. We consider the action of $G$ on sections of a homogeneous line bundle over $Ω$ and the corresponding eigenspaces of $G$-invariant differential operators. The Poisson transform maps hyperfunctions on the $S$ to the eigenspaces. We characterize the image in terms of twisted Hua operators. For some special parameters the Poisson transform is of Szegö type mapping into the relative discrete series; we compute the corresponding elements in the discrete series.

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BibTeX RIS

Khalid Koufany, Genkai Zhang. 2011-05-30. Hua operators, Poisson transform and relative discrete series on line bundle over bounded symmetric domains. https://arxiv.org/abs/1105.3806

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