The test function space is defined by $\mathscr{T} = \mathscr{T}(\mathbb{R}^{n})$ to be all functions of the class $C^{\infty}(\mathbb{R}^{n})$ which decreases as $x \rightarrow +\infty$, together with all their derivatives, faster than any power of $|x|^{-1}$.
Continuity in $\mathscr{T}$ is defined by saying that the sequence $\phi_{1}, \phi_{2}, \ldots , $ belonging to $\mathscr{T}$ converges to the function $\phi \in \mathscr{T}$, $\phi_{k} \rightarrow \phi$ as $k \rightarrow \infty$ in $\mathscr{T}$, if for all $\alpha$ and $\beta$
$$x^{\beta} D^{\alpha}\phi_{k}(x) \implies x^{\beta}D^{\alpha}\phi(x), \quad k \rightarrow \infty, \quad x \in \mathbb{R}^{n}.$$
Since the test functions belonging to $\mathscr{T}$ are absolutely integrable over $\mathbb{R}^{n}$, we define the operation of the Fourier transform $F$ over them by
$$F[\phi](\xi) := \int \phi(x)e^{i(\xi, x)} dx, \quad \phi \in \mathscr{T}.$$
I do not understand what the notation in the exponent means i.e. $i(\xi, x)$. I am unsure whether I forgot something trivial about notations?