Abstract

We introduce the notion of rationality for hyperholomorphic functions (functions in the kernel of the Cauchy–Fueter operator). Following the case of one complex variable, we give three equivalent definitions: the first in terms of Cauchy–Kovalevskaya quotients of polynomials, the second in terms of realizations and the third in terms of backward-shift invariance. Also introduced and studied are the counterparts of the Arveson space and Blaschke factors.

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