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 a homogeneous Cauchy problem on involving the differencial-difference operator .
arXiv preprint: http://arxiv.org/abs/1304.7191v2
Related arXiv preprints:
- (Discrete) Almansi Type Decompositions: An umbral calculus framework based on symmetries–http://arxiv.org/abs/1102.5434.
- Fischer Decomposition for Difference Dirac Operators–http://arxiv.org/abs/math/0609823.
- Flashback-”On a correspondence principle between discrete differential forms, graph structure and multi-vector calculus on symmetric lattices”
- New families of Special Functions on the lattice within Hypercomplex Variables-In Preparation.