Abstract
The even subgroup of the Weyl group associated with the crystallographic root system \(A_1 \times A_1\) 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 \(A_1 \times A_1\) 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.
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The authors gratefully acknowledge support from the Czech Science Foundation (GAČR), Grant No. 19-19535S.
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GC, JH and JT contributed to the main manuscript text, JH and JT prepared the figures. All authors reviewed the manuscript.
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Chadzitaskos, G., Hrivnák, J. & Thiele, J. Discrete even Fourier–Weyl transforms of \(A_1 \times A_1\). Anal.Math.Phys. 13, 76 (2023). https://doi.org/10.1007/s13324-023-00840-8
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DOI: https://doi.org/10.1007/s13324-023-00840-8