Rational Hyperholomorphic Functions in R4

Authors

Daniel Alpay, Chapman UniversityFollow
Michael Shapiro, E.S.F.M. del I.P.N.
Dan Volok, Ben Gurion University of the Negev

Document Type

Article

Publication Date

2005

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.

Comments

NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, volume 221, in 2005. DOI: 10.1016/j.jfa.2004.07.012

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Recommended Citation

D. Alpay, M. Shapiro and D. Volok. Rational hyperholomorphic functions in R4. Journal of Functional Analysis, vol. 221 (2005) pp. 122-149.

Peer Reviewed

1

Copyright

Elsevier

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.