Remark 12.4.12.label The Laplacian can be expressed as $\la=\sums{n}{i=1}\pd_{i}^{2}$. One can use the Fourier transform to characterize the linear operator $L=\sums{}{\al}c_{\al}(x)\pd^{\al}$ that commute with translation and rotation. So for all $f\in C^{\infty}$ and $T:\R^{n}\to\R^{n}$ we have $(Lf)\circ T=L(f\circ T)$.