Home » research » New families of Special Functions on the lattice within Hypercomplex Variables-In Preparation.

# New families of Special Functions on the lattice within Hypercomplex Variables-In Preparation.

This paper introduce new families of special functions of hypercomplex variable, based on a Lie algebra structure carrying a set of canonical operators on the lattice $h\mathbb{Z}^n$ which are Clifford-valued.

Using a minimal amount of the theory of finite differences and the basic elements of the theory of discrete quantum mechanics, we show that these special functions yield as eigenfunctions of a certain Jacobi-type operator on $h\mathbb{Z}^n$.
Although this approach is different from the ones presented by other authors within this subject, it offers a reliable way to formulate discrete function theories in the context of Clifford analysis, without requiring a-priori any kind of (skew-)Weyl algebra relations for the creation and annihilation operators.

1. […] New families of Special Functions on the lattice within Hypercomplex Variables-In Preparation. […]

2. […] provides me the doctor degree in mathematics (March 26, 2009).  In a couple of weeks I wish to disseminate some new material with the goal to continue developing the discrete Clifford analysis […]

3. […] New families of Special Functions on the lattice within Hypercomplex Variables-In Preparation. […]