Discrete $E$-transforms of $A_1 \times A_1$
The reducible crystallographic root system $A_1 \times A_1$, together with the even subgroup of the associated Weyl group, determines two-variable even Weyl orbit functions. These $E$-functions form the kernels of the developed discrete Fourier-Weyl $E$-transforms with the finite point and label sets realized by rectangular fragments of the admissibly shifted weight lattices. General form of the sixteen types of the point and label sets along with related discrete orthogonality relations of the $E$-functions are presented. The forward and backward transforms as well as the linked interpolation formulas and orthogonal transform matrices are exemplified. This is a joint work with Goce Chadzitaskos and Jan Thiele.