Skip to main content
SpringerLink
Log in

Clifford analysis and its applications. I. Representations of laplace operators. Regularity criteria. Integral representations of cauchy-green type

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

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

References

  1. M. P. Burlakov, “Clifford structure on manifolds”, In:Itogi Nauki i Techniki, Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Geometriya-3, Vol. 30, VINITI, Moscow (1995), pp. 205–257.

    Google Scholar 

  2. M. P. Burlakov,Differential Clifford algebras of space-time, Deposited at the All-Russian Institute for Scientific and Technical Information (1984).

  3. M. P. Burlakov and V. V. Pokazeev, “On some integral representations of solutions for spin equations in field theory,” In:Gravitation and Relativity Theory, Vol. 29, Kazan (1992), pp. 23–31.

  4. M. P. Burlakov and V. V. Pokazcev, “Algebra of differential forms in Kaluza space,” In:Differential Geometry of the Varieties of Figures, Vol. 25, Kaliningrad (1994), pp. 23–28.

  5. M. P. Burlakov, V. V. Pokazeev and L. E. Freidenzon, “Intergral representations of functions with values in Dirac algebra,” In:Current Questions in the Theory of Boundary Problems and Their Applications, Cheboksary (1988). pp. 18–22.

  6. M. P. Burlakov, V. V. Pokazeev and L. E. Freidenzon.Clifford analysis I. Clifford Δ-algebras, Deposited at the All-Russian Institute for Scientific and Technical Information Groznyi (1988).

  7. M. P. Burlakov, V. V. Pokazeev and L. E. Freidenson,Clifford analysis II. Integral representations of functions with values in Clifford algebra, Deposited at the All-Russian Institute for Scientific and Technical Information, Groznyi (1988).

  8. V. V. Vishnevskii, A. P. Shirokov and V. V. Shurygin,Spaces over Algebras, Kazan Univ. Press, Kazan (1985).

    Google Scholar 

  9. M. Karoubi,K-Theory. Introduction [Russian translation], Mir, Moscow (1981).

    Google Scholar 

  10. S. P. Kuznetsov, “OnB-sets in Clifford algebras,” In:Investigations on Boundary Problems and Their Applications, Cheboksary (1992), pp. 91–98.

  11. S. P. Kuznetsov and V. V. Mochalov,Internal automorphisms of Clifford algebras and strong regular functions, Deposited at the All-Russian Institute for Scientific and Technical Information, Cheboksary (1991).

  12. L. Raider,Quantum Field Theory [Russian translation], Mir, Moscow (1987).

    Google Scholar 

  13. B. A. Rozenfeld,Non-Euclidean Geometries [in Russian], Gostekhizdat, Moscow (1954).

    Google Scholar 

  14. P. Bosshard,Die Cliffordschen Zahlen, ihre Algebra und ihre Funktionentheorie [Thesis], Universität Zürich (1940).

  15. F. Brackx, “Integral representations and related series expansion for nullsolution of generalized Cauchy-Riemann systems in Euclidean space,”Wiss. Beitr. M. Luther Univ. Halle-Wittenberg, M, No. 35, 100 (1984).

    Google Scholar 

  16. F. Brackx, R. Delanghe, and F. Sommen,Clifford Analysis, Pitnam Publ. Inc., Boston-London-Melbourne (1982).

    Google Scholar 

  17. W. Clifford,Collected Mathematical Papers, Chelsea (reprint) (1968).

  18. Clifford Algebras and Their Applications in Mathematical Physics.Proc. 3rd Int. Conf., Deinze 1993 (F. Brackx, R. Delanghe, and H. Serras, Eds.)Fundamental Theories of Physics, Vol. 183, Kluwer Acad. Publ. Group, Dordrecht (1993).

    Google Scholar 

  19. R. Delanghe and F. Brackx “Runges theorem in hypercomplex function theory,”J. Approx. Theory,29, No. 3, 200–211 (1987).

    Article  MathSciNet  Google Scholar 

  20. R. Delanghe and F. Brackx, “Duality in hypercomplex function theory,”J. Funct. Anal. 37, No. 2, 164–181 (1980).

    Article  MATH  MathSciNet  Google Scholar 

  21. P. A. M. Dirac, “The quantum theory of the electron”Proc. Royal Soc. A 117, 610–624 (1928).

    MATH  Google Scholar 

  22. R. Fueter, “Zur Theorie der regularen Funktionen einer Quaternionenvariablen,”Monats. Math. Phys.,43, 69–74 (1936).

    Article  MATH  Google Scholar 

  23. B. Goldschmidt, “Existence theorems for overdetermined systems of partial differential equations of first order,”Math. Nach. 116, 233–250 (1984).

    MATH  MathSciNet  Google Scholar 

  24. H. Grassman,Gesammelte Mathematishe und Physikalishe Werke. Bd. 1, Tl.1–2, Lpz. (1894–96).

    Google Scholar 

  25. H. Hafeli, “Quaternionnengeometrie und das Abblidungsproblem der regularen Quaternionenfunktionen,”Commun. Math. Helv.,17, No. 2, 135–164 (1944).

    MathSciNet  Google Scholar 

  26. P. Lounesto, “Spinor valued regular functions,”Contemp. Math.,11, 155–175 (1982).

    MATH  Google Scholar 

  27. W. Nef, “Die Funktionentheorie der partiellen Differentialgleichungen zweiter Ordnung (Hypercomplex Funktionentheorie)”.Bull. Soc. Fribourge Sci. Nat. 37, 348–375 (1944).

    MathSciNet  Google Scholar 

  28. W. Pauli, “Zur Quantenmechanik des magnetischen Electrons”,Z. Phys.,43, 601–625 (1927).

    Article  Google Scholar 

  29. J. Ryan, “Extensions of Clifford analysis to complex. finite dimensional associative algebras with identity”.Proc. Roy. Irish. Acad.,A84, No 1, 37–50 (1984).

    MATH  MathSciNet  Google Scholar 

  30. J. Ryan, “Applications of Clifford analysis to axially symmetric partial differential equations,”Complex Variables: Theory Appl.,16, Nos. 2-3, 137–151 (1991).

    MATH  MathSciNet  Google Scholar 

  31. F. Sommen, “Monogenic functions on surfaces,”J. Reine Angew. Math., 145–161 (1985).

Download references

Authors
  1. V. A. Golubeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. V. Pokazeev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Itogi Naukii Tekhniki, Seriya Sovremennaya Matematikai Ee Prilozheniya. Tematicheskie Obzory. Vol. 37. Analysis 10. 1996.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Golubeva, V.A., Pokazeev, V.V. Clifford analysis and its applications. I. Representations of laplace operators. Regularity criteria. Integral representations of cauchy-green type. J Math Sci 91, 3258–3292 (1998). https://doi.org/10.1007/BF02433804

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02433804

Keywords

Search

Navigation