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 -