A Paley–Wiener theorem for reductive symmetric spaces


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.


Erik P. van den Ban

Mathematisch Instituut, Universiteit Utrecht, 3508 Utrecht, Netherlands

Henrik Schlichtkrull

Matematisk Institut, København Universitet, 2100 København Ø, Denmark