BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Chiara de Fabritiis (Università Politecnica delle Marche\, Italy) DTSTART:20210427T130000Z DTEND:20210427T140000Z DTSTAMP:20260422T201503Z UID:CAvid/38 DESCRIPTION:Title: * -products\, *-exponential\, *-logarithm: some peculiarities of slice regul ar functions on the quaternions\nby Chiara de Fabritiis (Università P olitecnica delle Marche\, Italy) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nSlice regular functions on qu aternions were introduced in 2006 by Gentili and Struppa in order to gener alize the notion of holomorphic functions on complex numbers (for an effec tive introduction you can refer to C. Stoppato's seminar (https://mediace ntral.ucl.ac.uk/Play/59248/). The theory had a quick development in severa l directions by many authors\, in this talk I will focus on three unexpect ed behaviours of these functions. The first aspect we deal with is the *-p roduct\, which is the analogous of pointwise product for holomorphic funct ions\; in particular we give an interpretation of this operation via two o perators which resemble the scalar product and the vector product on R^3. The second point we investigate is a suitable extension of the notion of e xponential of a slice regular function\, namely the *-exponential exp_*(f) (originally introduced by Colombo\, Sabadini and Struppa)\; we will descr ibe some of its features\, especially with regard to the non-commutativity of the *-product and to its connections with *-sine and *-cosine. Lastly\ , we study the possible existence and uniqueness of a *-logarithm of a nev er vanishing slice regular function\, both on slice and on product domains of the quaternions. We give some existence and non-existence results for *-logarithm of never-vanishing slice regular functions (according to the s plitting in real and vectorial part) and an accurate description of the po ssible uniqueness of the *-logarithm.\nThis is a joint work with Amedeo Al tavilla (Università di Bari).\n LOCATION:https://researchseminars.org/talk/CAvid/38/ END:VEVENT END:VCALENDAR