2018/01/04 by Amedeo Altavilla, A. Altavilla, Chiara de Fabritiis +1 · 9 citations
Computer Science · Mathematics · #Algebraic and Geometric Analysis #Factorization #Function (biology) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Product (mathematics) #Property (philosophy) #Scalar (mathematics) #Wafer #math.CV #msc:16D40 #msc:30G35 #msc:30H50 #msc:32A30
paper · pdf · doi:10.1007/s10231-018-0724-1
published in Annali di Matematica Pura ed Applicata (1923 -) 197(4), 1269-1294 (Springer Science+Business Media) · 23 pages, to appear in Annali di Matematica Pura e Applicata
arxiv created 2018/01/04 · openalex created_date 2018/01/12 · openalex publication_date 2018/01/28 · arxiv updated 2019/01/03 · openalex updated_date 2026/08/05
We study global properties of quaternionic slice regular functions (also called s-regular) defined on symmetric slice domains. In particular, thanks to new techniques and points of view, we can characterize the property of being one-slice preserving in terms of the projectivization of the vectorial part of the function. We also define a "Hermitian" product on slice regular functions which gives us the possibility to express the *-product of two s-regular functions in terms of the scalar product of suitable functions constructed starting from f and g. Afterwards we are able to determine, under different assumptions, when the sum, the *-product and the *-conjugation of two slice regular functions preserve a complex slice. We also study when the *-power of a slice regular function has this property or when it preserves all complex slices. To obtain these results we prove two factorization theorems: in the first one, we are able to split a slice regular function into the product of two functions: one keeping track of the zeroes and the other which is never-vanishing; in the other one we give necessary and sufficient conditions for a slice regular function (which preserves all complex slices) to be the symmetrized of a suitable slice regular one.