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Regular Functions on the Scaled Hypercomplex Numbers
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 \(\mathbb {R}\).
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