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Rational hyperholomorphic functions in (\mathbb R^4)

D. Alpay·M. Shapiro·D. Volok
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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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D. Alpay, M. Shapiro, D. Volok. 2003-12-30. Rational hyperholomorphic functions in (\mathbb R^4). https://arxiv.org/abs/math/0312504

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