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The Clifford–Cauchy transform with a continuous density: N. Davydov's theorem
Author(s) -
AbreuBlaya Ricardo,
BoryReyes Juan,
Gerus Oleg F.,
Shapiro Michael
Publication year - 2004
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.594
Subject(s) - mathematics , lipschitz continuity , cauchy distribution , cauchy's integral formula , cauchy's integral theorem , clifford analysis , cauchy problem , pure mathematics , mathematical analysis , initial value problem , dirac operator
N. A. Davydov was among the first mathematicians who investigated the question of the continuity of the complex Cauchy transform along a non‐smooth curve. In particular he proved that the Cauchy transform over an arbitrary closed, rectifiable Jordan curve can be continuously extended up to this curve from both sides if its density belongs to the Lipschitz class. In this paper we deal with higher dimensional analogue of Davydov's theorem within the framework of Clifford analysis. Copyright © 2005 John Wiley & Sons, Ltd.