Hardy space on the metaplectic semigroup. (Espace de Hardy sur le semi-groupe métaplectique.) (French) Zbl 0880.22003

Summary: We show that the odd part of the Hardy space on the metaplectic semigroup \(\widetilde\Gamma\) is isomorphic to the classical Hardy space on the tube domain \(Sp (2m, \mathbb{R})/U(2m)\). We also compute the corresponding Cauchy-Szegö kernel and decompose \(H^2(Sp (2m, \mathbb{R})/U(2m))\) under the action of \(Mp (m,\mathbb{R}) \times Mp (m, \mathbb{R})\).


22E30 Analysis on real and complex Lie groups
43A17 Analysis on ordered groups, \(H^p\)-theory
46E15 Banach spaces of continuous, differentiable or analytic functions