TY - JOUR
T1 - The isotonic Cauchy transform
AU - Blaya, Ricardo Abreu
AU - Reyes, Juan Bory
AU - Peña, Dixan Peña
AU - Sommen, Frank
N1 - Funding Information:
This paper was written while the second named author was visiting the Department of Mathematical Analysis of Ghent University. He was supported by a Special Research Fund No. 01T13804 which has been obtained for collaboration between the Clifford research group in Ghent and the Cuban research group in Clifford analysis, on the subject of Boundary value theory in Clifford Analysis. Juan Bory Reyes wishes to thank all members of this Department for their kind hospitality. Dixan Peña Peña was supported by a Doctoral Grant of the Special Research Fund of Ghent University. He would like to express his sincere gratitude.
PY - 2007/5
Y1 - 2007/5
N2 - Starting with an integral representation for the class of continuously differentiable solutions f : ℝ2n, → ℂ0,n of the system ∂x1 f + if̃∂x2 = 0 where ℂ0,n is the complex Clifford algebra constructed over ℝn, x1, x2 are some suitable Clifford vectors and ∂x1, ∂x2 their corresponding Dirac operators, we define the isotonic Cauchy transform and establish the Sokhotski-Plemelj formulae. Some consequences of this result are also derived.
AB - Starting with an integral representation for the class of continuously differentiable solutions f : ℝ2n, → ℂ0,n of the system ∂x1 f + if̃∂x2 = 0 where ℂ0,n is the complex Clifford algebra constructed over ℝn, x1, x2 are some suitable Clifford vectors and ∂x1, ∂x2 their corresponding Dirac operators, we define the isotonic Cauchy transform and establish the Sokhotski-Plemelj formulae. Some consequences of this result are also derived.
KW - Clifford analysis
KW - Isotonic functions
KW - Sokhotski-Plemelj formulae
UR - http://www.scopus.com/inward/record.url?scp=34249071106&partnerID=8YFLogxK
U2 - 10.1007/s00006-007-0025-z
DO - 10.1007/s00006-007-0025-z
M3 - Artículo
AN - SCOPUS:34249071106
SN - 0188-7009
VL - 17
SP - 145
EP - 152
JO - Advances in Applied Clifford Algebras
JF - Advances in Applied Clifford Algebras
IS - 2
ER -