Skip to main content
SpringerLink
Log in

Representation of Weinstein k-Monogenic Functions by Differential Operators

  • Published:
Complex Analysis and Operator Theory Aims and scope Submit manuscript

Abstract

This paper deals with a type of generalized monogenic functions in Clifford analysis, the so-called Weinstein k-monogenic function. We will give an explicit representation of the Weinstein k-monogenic functions by differential operators of Bauer’s type in the cases \(k=2m,m\in {\mathbb {N}}^*\).

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. Bauer, K.W., Ruscheweyh, S.T.: Differential Operators for Partial Differential Equations and Function Theoretic Applications. Lecture Notes in Mathematics, p. 791 (1980)

    Chapter  Google Scholar 

  2. Beltrami, E.: Opere Matematiche, vol. 3, pp. 349–382. Milano, Hoepli (1911)

    Google Scholar 

  3. Berglez, P.: Representation of pseudoanalytic functions in the space. In: More Progresses in Analysis, pp. 1119–1126. World Scientific Publishing Co., Singapore (2008)

  4. Bers, L., Gelbart, A.: On a class of differential equations in mechanics of continua. Q. Appl. Math. 1, 168–188 (1943)

    Article  MathSciNet  Google Scholar 

  5. Brackx, F., Delanghe, R., Sommen, F.: Clifford Analysis. Research Notes in Mathematics, vol. 76. Pitman (Advanced Publishing Program), Boston (1982)

    MATH  Google Scholar 

  6. Brackx, F., Delanghe, R.: On harmonic potential fields and the structure of monogenic functions. J. Anal. Appl. 22(2), 261–273 (2003)

    MathSciNet  MATH  Google Scholar 

  7. Brackx, F., Delanghe, R., Sommen, F.: On conjugate harmonic functions in Euclidean space. Math. Methods Appl. Sci. 25, 1553–1562 (2002)

    Article  MathSciNet  Google Scholar 

  8. Delanghe, R.: On primitives of monogenic functions. Complex Var. Elliptic Equ. 51(8–11), 959–970 (2006)

    Article  MathSciNet  Google Scholar 

  9. Diaz, J.B., Weinstein, A.: On the Fundamental Solutions of a Singular Beltrami Operator. Studies in Mathematics and Mechanics Presented to R, vol. Mises, pp. 98–102. Academic Press, New York (1954)

    Google Scholar 

  10. Dinh, D.C.: Weinstein \(k\)-monogenic functions in Clifford analysis. Adv. Appl. Clifford Algebras (to appear)

  11. Eriksson, S.-L., Leutwiler, H.: Contributions to the theory of hypermonogenic functions. Complex Var. Elliptic Equ. 51(5–6), 547–561 (2006)

    Article  MathSciNet  Google Scholar 

  12. Eriksson, S.-L., Orelma, H., Sommen, F.: Vekua systems in hyperbolic harmonic analysis. Complex Anal. Oper. Theory 10(2), 251–265 (2016)

    Article  MathSciNet  Google Scholar 

  13. Weinstein, A.: Generalized axially symmetric potential theory. Bull. Am. Math. Soc. 69, 20–38 (1953)

    Article  MathSciNet  Google Scholar 

  14. Weinstein, A.: Discontinuous integrals and generalized potential theory. Trans. Am. Math. Soc. 63, 342–354 (1948)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam

    Doan Cong Dinh

  2. Faculty of Information Technology, National University of Civil Engineering, Hanoi, Vietnam

    Luong Thi Tuyet

Authors
  1. Doan Cong Dinh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luong Thi Tuyet
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Doan Cong Dinh.

Additional information

Communicated by Daniel Aron Alpay.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the topical collection “Higher Dimensional Geometric Function Theory and Hypercomplex Analysis” edited by Irene Sabadini, Michael Shapiro and Daniele Struppa.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dinh, D.C., Tuyet, L.T. Representation of Weinstein k-Monogenic Functions by Differential Operators. Complex Anal. Oper. Theory 14, 20 (2020). https://doi.org/10.1007/s11785-020-00980-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11785-020-00980-w

Keywords

Mathematics Subject Classification

Search

Navigation