UIR	Unitary Irreducible Representation
G	The rigid body motions group $SE\left(3\right)$	Equation (1)
$\mathbf{a}$	The reference axis $\mathbf{a}={\mathbf{e}}_z={(0,0,1)}^T$	Equation (3)
H	The subgroup that stabilizes $(\mathbf{0},\mathbf{a})$	Equation (3)
$G/H$	The homogeneous space of positions and orientations ${\mathbb{R}}^3⋊S^2$	Equation (3)
$\overline{U}$	The spatial Fourier transform of U	Equation (18)
$\widehat{U}$	The Fourier transform $\widehat{U}={\mathcal{F}}_{G/H}U$	Equation (43)
$\alpha$	Parameter of the $\alpha$-Stable processes (indexing fractional power of the generator)	Equation (10)