English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Fueter theorem provides a two step procedure to build an axiallymonogenic function, i.e. a null-solutions of the Cauchy-Riemann operator in $\mathbb{R}^4$, denoted by $ \mathcal{D}$. In the first step a holomorphicfunction is extended to a slice hyperholomorphic function, by means of theso-called slice operator. In the second step a monogenic function is built byapplying the Laplace operator in four real variables ($\Delta$) to the slicehyperholomorphic function. In this paper we use the factorization of theLaplace operator, i.e. $\Delta= \mathcal{\overline{D}} \mathcal{D}$ to splitthe previous procedure. From this splitting we get a class of functions thatlies between the set of slice hyperholomorphic functions and the set of axiallymonogenic functions: the set of axially polyanalytic functions of order 2, i.e.null-solutions of $ \mathcal{D}^2$. We show an integral representation formulafor this kind of functions. The formula obtained is fundamental to define theassociated functional calculus on the $S$-spectrum. As far as the authors know,this is the first time that a monogenic polyanalytic functional calculus hasbeen taken into consideration.

A polyanalytic functional calculus of order 2 on the S-spectrum