Skip to main content
SpringerLink
Log in

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

  • Published:
Advances in Applied Clifford Algebras Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Di Teodoro A., Vanegas C.: Fundamental solutions for the first orden metamonogenic operator. Adv. Appl. Clifford Algebras 22(1), 49–58 (2011)

    Article  MathSciNet  Google Scholar 

  2. R. Feynman, R. Leighton and M. Sands, The Feynman Lectures on Physics: Definitive and Extended Edition. Addison Wesley, (2005). Cauchy–Pompeiu Formula and its Applications

  3. C. Miranda, Partial Differential Equations of Elliptic Type. Springer–Verlag Berlin, (1970).

  4. J. Jackson, Classical Electrodynamics. Wiley, (1998).

  5. W. Tutschke and C. Vanegas, General algebraic structures of Clifford type and Cauchy–Pompeiu formulae for some piecewise constant structure relations. Adv. Appl. Clifford Algebras 21 (4) (2011), 829–838.

    Google Scholar 

  6. W. Tutschke and C. Vanegas, Clifford algebras depending on parameters and their applications to partial differential equations. Some topics on value distribution and differentiability in complex and p–adic analysis. Beijing: Science Press. Mathematics Monograph Series 11 (2008), 430–450.

  7. W. Tutschke and C. Vanegas, Métodos del análisis complejo en dimensiones superiores. XXI Escuela Venezolana de Matem´aticas, Ediciones IVIC, (2008).

  8. Mustafa E., Cohen J.: Hertz and Debye potentials and electromagnetic fields in general relativity. Class. Quantum Grav 4, 1623–1631 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  9. Xu Zhenyuan, A function theory for the operator D — λ. Complex Variables, Theory and Application: An International Journal 16 (1) (1991), 27–42.

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática, Universidad Simón Bolívar, Valle de Sartenejas, Caracas, Venezuela

    Antonio Di Teodoro & Adrián Infante

Authors
  1. Antonio Di Teodoro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adrián Infante
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonio Di Teodoro.

Additional information

This work was completed with the support of Departamento de Matemática Universidad Simón Bolĺvar. Caracas, Venezuela.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Teodoro, A.D., Infante, A. A Cauchy–Pompeiu Representation Formula Using Dirac Operator and its Applications in Some Piecewise Constant Structure Relations. Adv. Appl. Clifford Algebras 23, 323–337 (2013). https://doi.org/10.1007/s00006-012-0372-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00006-012-0372-2

Keywords

Search

Navigation