Image of Schwartz Space Under Spectral Projection

Details Image of Schwartz Space Under Spectral Projection Image of Schwartz Space Under Spectral Projection

2007-12-26

arxiv.org/abs/0712.4117v3

Mathematics

Representation Theory

21 pages,V2

Scientific paper

Let $X= G/K$ symmetric space of non compact type, where $G$ is a rank-one connected semisimple Lie group with finite center. We shall look at the transform $ P_\lambda f(x) = f \ast \varphi_\lambda(x)$, where, $\lambda \in \mathbb C$ and $\varphi_\lambda$ is the elementary spherical function. We shall try to characterizes the image of the Schwartz spaces $S^p(X) $ where $0 < p \leq 2$ under the above transform.

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