Special Functions of Hypercomplex Variable on the Lattice Based on SU(1,1) - Faustino, Nelson (Symmetry, integrability and geometry, methods and applications, 2013)
Based on the representation of a set of canonical operators on the lattice [...], which are Clifford-vector-valued, we will introduce new families of special functions of hypercomplex variable possessing [...] symmetries. The Fourier decomposition of the space of Clifford-vector-valued polynomials with respect to the [...]-module gives rise to the construction of new families of polynomial sequences as eigenfunctions of a coupled system involving forward/backward discretizations [...] of the Euler operator [...]. Moreover, the interpretation of the one-parameter representation [...] of the Lie group [...] as a semigroup [...] will allows us to describe the polynomial solutions of an homogeneous Cauchy problem on [...] involving the differencial-difference operator [...]. [ProQuest: [...] denotes formulae omitted.]