Meaning of $(\nabla_x + \nabla_\xi)^n$ what does $(\nabla_x + \nabla_\xi)^n$ mean? (In the context, $x,\xi\in \mathbb{R}^d$). In my notes, the author states this should be a tensor, but what exactly does he mean. Is this clear notation?
My operator acts on a function $f:\,\mathbb{R}^d\times\mathbb{R}^d \to \mathbb{R}$.
So in one dimensions, this is $(\partial_x + \partial_\xi)^n f$.
Note, the dimension is $d$ and in general $d\neq n$.

It is meant that $n$ is dimension of the tensor. This means that $$\left((\nabla _x )^n\right)_{i_1,\dots i_n}  =\partial_{x_{i_1}}\dots \partial_{x_{i_n}}$$  where $i_j \in \{1,\dots d\}$ for $j\in\{1,\dots, n\}$.
