Skip to main content
Log in

On hyperholomorphic functions of the space variable

  • Published:
Ukrainian Mathematical Journal Aims and scope

For quaternionic-differentiable functions of the space variable, we prove the theorem on the integral over a closed surface which is an analog of the Cauchy theorem from complex analysis.

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

Access this article

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. G. C. Moisil and N. Theodoresco, “Functions holomorphes dans l’espace,” Mathematica (Cluj), 5, 142–159 (1931).

    MATH  Google Scholar 

  2. A. V. Bitsadze, Boundary-Value Problems for the Second-Order Elliptic Equations [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  3. R. Fueter, “Die Funktionentheorie der Differentialgleichungen Δu = 0 und ΔΔu = 0 mit vier reellen Variablen,” Commun. Math. Helv., 8, 371–378 (1936).

    Article  MathSciNet  Google Scholar 

  4. V. V. Kravchenko and M. V. Shapiro, Integral Representations for Spatial Models of Mathematical Physics, Longman, Harlow (1996).

    MATH  Google Scholar 

  5. K. Gürlebeck and W. Sprössig, Quaternionic and Clifford Calculus for Physicists and Engineers, Wiley, Chichester (1997).

    MATH  Google Scholar 

  6. A. Sudbery, “Quaternionic analysis,” Math. Proc. Cambridge Phil. Soc., 85, 199–225 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  7. V. V. Kravchenko, Applied Quaternionic Analysis, Heldemann, Berlin (2003).

    MATH  Google Scholar 

  8. B. V. Shabat, Introduction to Complex Analysis. Part 1. Functions of One Variable [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  9. A. S. Meilikhzon, “On the monogeneity of quaternions,” Dokl. Akad. Nauk SSSR, 59, No. 3, 431–434 (1948).

    Google Scholar 

  10. J. Cnops, An Introduction to Dirac Operators on Manifolds, Birkhaüser, Boston (2002).

    Book  MATH  Google Scholar 

  11. R. A. Blaya, J. B. Reyes, and M. Shapiro, “On the Laplacian vector fields theory in domains with rectifiable boundary,” Math. Meth. Appl. Sci., 29, 1861–1881 (2006).

    Article  MATH  Google Scholar 

  12. O. F. Gerus and M. V. Shapiro, “On a Cauchy-type integral related to the Helmholtz operator in the plane,” Bol. Soc. Mat. Mexic., 10, No. 1, 63–82 (2004).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 4, pp. 459–465, April, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Herus, O.F. On hyperholomorphic functions of the space variable. Ukr Math J 63, 530–537 (2011). https://doi.org/10.1007/s11253-011-0521-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-011-0521-0

Keywords

Navigation