Discrete even Fourier-Weyl transforms of A₁ x A₁

The even subgroup of theWeyl group associated with the crystallographic root system A(1) x A(1) induces two-variable even Weyl orbit functions which form the kernels of the developed discrete Fourier-Weyl transforms. The finite point and label sets of the discrete trigonometric transforms are formed by rectangular fragments of the A(1)x A(1) admissibly shifted weight lattices in the Euclidean plane. Sixteen types of the point and label sets are listed and the related discrete orthogonality relations of the even Weyl orbit functions are demonstrated. The forward and backward transforms together with the linked interpolation formulas and orthogonal transform matrices are presented and exemplified.