Quaternionic regularity and the dibar-Neumann problem in C^2
| dc.creator | Perotti, Alessandro | |
| dc.date | 2006-12-04 | |
| dc.date | 2006-12-13 | |
| dc.date.accessioned | 2026-07-07T06:43:11Z | |
| dc.date.available | 2026-07-07T06:43:11Z | |
| dc.description | Let D be a domain in the quaternionic space H. We prove a differential criterion that characterizes Fueter-regular quaternionic functions f:bD -> H of class C^1. We find differential operators T and N, with complex coefficients, such that a function f is regular on D if and only if (N-jT)f=0 on the boundary of D (j a basic quaternion) and f is harmonic on D. As a consequence, by means of the identification of H with C^2, we obtain a non-tangential holomorphicity condition which generalizes a result of Aronov and Kytmanov. We also show how the differential criterion and regularity are related to the dibar-Neumann problem in C^2. | |
| dc.description | 13 pages; added references; small changes. To appear on Complex Variables and Elliptic Equations | |
| dc.identifier | https://arxiv.org/abs/math/0612092 | |
| dc.identifier | http://arxiv.org/abs/math/0612092 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102318 | |
| dc.subject | Complex Variables | |
| dc.subject | 32A30 | |
| dc.title | Quaternionic regularity and the dibar-Neumann problem in C^2 | |
| dc.type | text |