Rational hyperholomorphic functions in (\mathbb R^4)
Functional Analysis
2007-05-23 v1 Complex Variables
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.
Cite
@article{arxiv.math/0312504,
title = {Rational hyperholomorphic functions in (\mathbb R^4)},
author = {D. Alpay and M. Shapiro and D. Volok},
journal= {arXiv preprint arXiv:math/0312504},
year = {2007}
}