A general setting for functions of Fueter variables: differentiability, rational functions, Fock module and related topics

Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We develop some aspects of the theory of hyperholomorphic functions whose values are taken in a Banach algebra over a field—assumed to be the real or the complex numbers—and which contains the field. Notably, we consider Fueter expansions, Gleason’s problem, the theory of hyperholomorphic rational functions, modules of Fueter series, and related problems. Such a framework includes many familiar algebras as particular cases. The quaternions, the split quaternions, the Clifford algebras, the ternary algebra, and the Grassmann algebra are a few examples of them.

Original languageEnglish
Pages (from-to)207-246
Number of pages40
JournalIsrael Journal of Mathematics
Volume236
Issue number1
DOIs
StatePublished - 1 Mar 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020, The Hebrew University of Jerusalem.

Funding

Ismael L. Paiva acknowledges financial support from the Science without Borders program (CNPq/Brazil). Daniel Alpay thanks the Foster G. and Mary McGaw Professorship in Mathematical Sciences, which supported this research.

FundersFunder number
CNPq/Brazil
Foster G. and Mary McGaw Professorship in Mathematical Sciences

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