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On the solutions of the Moisil–Théodoresco system
Author(s) -
Reyes Juan Bory,
Delanghe Richard
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.980
Subject(s) - mathematics , generalization , real line , pure mathematics , cauchy distribution , line (geometry) , algebra over a field , mathematical analysis , geometry
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.
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