In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative *-algebra A over R. These recently introduced function theories generalize to higher dimensions the classical theory of functions of a complex variable. Slice functions over A, which comprise all polynomials over A, form an alternative *-algebra themselves when endowed with appropriate operations. We presently study this algebraic structure in detail and we confront questions about the existence of multiplicative inverses. This study leads us to a detailed investigation of the zero sets of slice functions and of slice regular functions, which are of course of independent interest.
The algebra of slice functions / Ghiloni, Riccardo; Perotti, Alessandro; Stoppato, Caterina. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 369:(2017), pp. 4725-4762. [10.1090/tran/6816]
The algebra of slice functions
STOPPATO, CATERINA
2017
Abstract
In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative *-algebra A over R. These recently introduced function theories generalize to higher dimensions the classical theory of functions of a complex variable. Slice functions over A, which comprise all polynomials over A, form an alternative *-algebra themselves when endowed with appropriate operations. We presently study this algebraic structure in detail and we confront questions about the existence of multiplicative inverses. This study leads us to a detailed investigation of the zero sets of slice functions and of slice regular functions, which are of course of independent interest.File | Dimensione | Formato | |
---|---|---|---|
16.TAMS.pdf
Accesso chiuso
Tipologia:
Pdf editoriale (Version of record)
Licenza:
Tutti i diritti riservati
Dimensione
464.84 kB
Formato
Adobe PDF
|
464.84 kB | Adobe PDF | Richiedi una copia |
AMSEarlyView-tran6816.pdf
accesso aperto
Tipologia:
Versione finale referata (Postprint, Accepted manuscript)
Licenza:
Tutti i diritti riservati
Dimensione
519.34 kB
Formato
Adobe PDF
|
519.34 kB | Adobe PDF |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.