Appell Bases for Monogenic Functions of Three Variables |
| |
Authors: | Cynthia Álvarez-Peña R Michael Porter |
| |
Institution: | 1. Depto. de Matemáticas, CINVESTAV, Querétaro, México
|
| |
Abstract: | Monogenic (or hyperholomorphic) functions are well known in general Clifford algebras but have been little studied in the particular case ${\mathbb{R}^{3} \rightarrow \mathbb{R}^{3}}$ R 3 → R 3 . We describe for this case the collection of all Appell systems: bases for the finite-dimensional spaces of monogenic homogeneous polynomials which respect the operator ${D = \partial_{0} - \vec{\partial}}$ D = ? 0 ? ? → . We prove that no purely algebraic recursive formula (in a specific sense) exists for these Appell systems, in contrast to the existence of known constructions for ${\mathbb{R}^{3} \rightarrow \mathbb{R}^{4}}$ R 3 → R 4 and ${\mathbb{R}^{4} \rightarrow \mathbb{R}^{4}}$ R 4 → R 4 . However, we give a simple recursive procedure for constructing Appell bases for ${\mathbb{R}^{3} \rightarrow \mathbb{R}^{3}}$ R 3 → R 3 which uses the operation of integration of polynomials. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|