Let (left(X_{t} ight)_{t geqslant 0}) be a (d)-dimensional Feller process and let (f, g in mathcal{C}_{infty}left(mathbb{R}^{d} ight)).

Let \(\left(X_{t}\right)_{t \geqslant 0}\) be a \(d\)-dimensional Feller process and let \(f, g \in \mathcal{C}_{\infty}\left(\mathbb{R}^{d}\right)\). Show that the function \(x \mapsto \mathbb{E}^{x}\left(f\left(X_{t}\right) g\left(X_{t+s}\right)\right)\) is also in 

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Coo (Rd).