A Cauchy-Pompeiu Representation Formula Using Dirac Operator and its Applications in Some Piecewise Constant Structure Relations

Antonio Di Teodoro; Adrián Infante

doi:10.1007/s00006-012-0372-2

A Cauchy-Pompeiu Representation Formula Using Dirac Operator and its Applications in Some Piecewise Constant Structure Relations

Antonio Di Teodoro
, Adrián Infante

Universidad Simón Bolívar

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	323-337
Number of pages	15
Journal	Advances in Applied Clifford Algebras
Volume	23
Issue number	2
DOIs	https://doi.org/10.1007/s00006-012-0372-2
State	Published - Jun 2013
Externally published	Yes

Keywords

Cauchy-Pompeiu formula
Clifford analysis
Fundamental solution
Integral representation
Structure relations of Clifford algebra

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10.1007/s00006-012-0372-2

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title = "A Cauchy-Pompeiu Representation Formula Using Dirac Operator and its Applications in Some Piecewise Constant Structure Relations",

abstract = "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.",

keywords = "Cauchy-Pompeiu formula, Clifford analysis, Fundamental solution, Integral representation, Structure relations of Clifford algebra",

author = "Teodoro, \{Antonio Di\} and Adri{\'a}n Infante",

note = "Funding Information: ∗Corresponding author This work was completed with the support of Departamento de Matem{\'a}tica Universidad Sim{\'o}n Bol{\'i}var. Caracas, Venezuela.",

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doi = "10.1007/s00006-012-0372-2",

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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 - https://www.scopus.com/pages/publications/84878039203

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 -

A Cauchy-Pompeiu Representation Formula Using Dirac Operator and its Applications in Some Piecewise Constant Structure Relations

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Keywords

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