The harmonicity of slice regular functions

by Cinzia Bisi (Università Degli Studi Di Ferrera)

Location: Campus Sterre, Building S8, Classroom 3.2, Ghent
Time: Friday September 14, 2018 at 14:30

I will start improving the definition of slice regular function over the quaternions given by Gentili-Struppa in 2006-2007, and of monogenic function over a real Clifford algebra introduced by Colombo-Sabadini-Struppa in 2009. Then, bringing new ideas to the theory, I will answer positively to the question: is a slice regular function over the quaternions (analogously to a holomorphic function over the complex) ”harmonic” in some sense, i.e. is it in the kernel of some order-two differential operator over the quaternions? Finally, I will deduce novel integral formulas as applications. This is part of a project with J. Winkelmann.