Rational hyperholomorphic functions in (\mathbb R^4)

Alpay, D.; Shapiro, M.; Volok, D.

Rational hyperholomorphic functions in (\mathbb R^4)

Authors

Alpay, D.

Shapiro, M.

Volok, D.

Description

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.