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Vanishing at infinity on homogeneous spaces of reductive type
Published online by Cambridge University Press: 15 April 2016
Abstract
Let $G$ be a real reductive group and
$Z=G/H$ a unimodular homogeneous
$G$ space. The space
$Z$ is said to satisfy VAI (vanishing at infinity) if all smooth vectors in the Banach representations
$L^{p}(Z)$ vanish at infinity,
$1\leqslant p<\infty$. For
$H$ connected we show that
$Z$ satisfies VAI if and only if it is of reductive type.
MSC classification
- Type
- Research Article
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- © The Authors 2016
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