Abstract
A new class of special functions of three real variables, based on the alternating subgroup of the permutation group S3, is studied. These functions are used for Fourier-like expansion of digital data given on lattice of any density and general position. Such functions have only trivial analogs in one and two variables; a connection to the E-functions of C3 is shown. Continuous interpolation of the three-dimensional data is studied and exemplified.
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