Regular Functions on the Scaled Hypercomplex Numbers

Abstract

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