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Algebras of invariant functions on the Šilov boundary of generalized half-planes

Author: Giovanna Carcano
Journal: Proc. Amer. Math. Soc. 111 (1991), 743-753
MSC: Primary 22E30; Secondary 32M15, 43A20
MathSciNet review: 1039253
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Abstract: Let $ \mathcal{N}$ be the nilpotent Lie group identified to the Šilov boundary of a symmetric generalized half-plane $ \mathcal{D}$ and $ L$ a compact group acting on $ \mathcal{N}$ by automorphisms, arising from the realization of $ \mathcal{D}$ as hermitian symmetric space. Is then $ (L \ltimes \mathcal{N},L)$ a Gelfand pair? We study the problem and resolve it in the case of classical families.

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Article copyright: © Copyright 1991 American Mathematical Society