Abstract:
We describe the structure of closed linear subspaces in some topological vector spaces that consist of functions on the exceptional non-compact symmetric space
$M=F_4/{\operatorname{Spin}(9)}$ (the Cayley space) and are invariant under the natural quasi-regular representation of the group $F_4$. The class of function spaces under consideration contains the spaces $C^d(M)$ of $d$-times continuously differentiable functions
($d=0,1,\dots,\infty$) and the spaces of functions of exponential growth on $M$.
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