On the solutions of the Moisil–Théodoresco system

✍ Scribed by Juan Bory Reyes; Richard Delanghe

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 128 KB
• Volume: 31
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.980

✦ Synopsis

Abstract

A structure theorem is proved for the solutions to the Moisil–Théodoresco system in open subsets of ℝ^3^. Furthermore, it is shown that the Cauchy transform maps L~2~(ℝ^2^, ℝ~0, 2~^+^) isomorphically onto H^2^(ℝ~+~^3^, ℝ~0, 3~^+^), thus proving an elegant generalization to ℝ^2^ of the classical notion of an analytic signal on the real line. Copyright © 2008 John Wiley & Sons, Ltd.