Regular Functions on the Scaled Hypercomplex Numbers

Abstract

In this paper, we study the regularity of \(\mathbb {R}\)-differentiable functions on open connected subsets of the scaled hypercomplex numbers \(\left\{ \mathbb {H}_{t}\right\} _{t\in \mathbb {R}}\) by studying the kernels of suitable differential operators \(\left\{ \nabla _{t}\right\} _{t\in \mathbb {R}}\), up to scales in the real field \(\mathbb {R}\).