Special Functions of Hypercomplex Variable on the Lattice Based on SU(1,1)

Based on the representation of a set of canonical operators on the lattice hZ, which are Clifford-vector-valued, we will introduce new families of special functions of hypercomplex variable possessing su(1, 1) symmetries. The Fourier decomposition of the space of Clifford-vector-valued polynomials with respect to the SO(n)× su(1, 1)-module gives rise to the construction of new families of polynomial sequences as eigenfunctions of a coupled system involving forward/backward discretizations E± h of the Euler operator E = n ∑