Rational hyperholomorphic functions in (\mathbb R^4)

Details Rational hyperholomorphic functions in (\mathbb R^4) Rational hyperholomorphic functions in (\mathbb R^4)

2003-12-30

arxiv.org/abs/math/0312504v1

Journal of Functional Analysis, vol. 221 (2005): 122-149

Mathematics

Functional Analysis

Scientific paper

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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