TY - JOUR
T1 - A Cauchy-Pompeiu Representation Formula Using Dirac Operator and its Applications in Some Piecewise Constant Structure Relations
AU - Teodoro, Antonio Di
AU - Infante, Adrián
N1 - Funding Information:
∗Corresponding author This work was completed with the support of Departamento de Matemática Universidad Simón Bolívar. Caracas, Venezuela.
PY - 2013/6
Y1 - 2013/6
N2 - In the present paper we use the piecewise constant structure relations of a Clifford algebra in order to obtain a Cauchy-Pompeiu representation for D - λ and D + λ operators, with these formulas we construct a distributional solutions for the equations that involves these operators with arbitrary right hand side. We also present an example where we build an integral representation for combinations of these operators.
AB - In the present paper we use the piecewise constant structure relations of a Clifford algebra in order to obtain a Cauchy-Pompeiu representation for D - λ and D + λ operators, with these formulas we construct a distributional solutions for the equations that involves these operators with arbitrary right hand side. We also present an example where we build an integral representation for combinations of these operators.
KW - Cauchy-Pompeiu formula
KW - Clifford analysis
KW - Fundamental solution
KW - Integral representation
KW - Structure relations of Clifford algebra
UR - http://www.scopus.com/inward/record.url?scp=84878039203&partnerID=8YFLogxK
U2 - 10.1007/s00006-012-0372-2
DO - 10.1007/s00006-012-0372-2
M3 - Artículo
AN - SCOPUS:84878039203
SN - 0188-7009
VL - 23
SP - 323
EP - 337
JO - Advances in Applied Clifford Algebras
JF - Advances in Applied Clifford Algebras
IS - 2
ER -