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A Paley-Wiener theorem for reductive symmetric spaces. (English) Zbl 1132.22010

Summary: Let \(X=G/H\) be a reductive symmetric space and \(K\) a maximal compact subgroup of \(G\). The image under the Fourier transform of the space of \(K\)-finite compactly supported smooth functions on \(X\) is characterized.

MSC:

22E30 Analysis on real and complex Lie groups
22E46 Semisimple Lie groups and their representations
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