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Generalized Monogenic Functions Satisfying Differential Equations with Anti-Monogenic Right-Hand Sides

  • W. Tutschke
  • U. Yüksel
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 6)

Abstract

A generalized monogenic function is a Clifford-algebra-valued solution u = u(x) of an equation of type Du = F(x,u) where D is the Cauchy-Riemann operator in n+1 and F(x,u) is linear in the components of u. The paper proves a sufficient condition under which the right-hand side is antimonogenic. This criterion makes it possible to construct anti-monogenic righthand sides.

Keywords

Transition Matrix Elliptic System Clifford Algebra Transition Matrice Monogenic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Bers, L.: Theory of pseudo-analytic functions. (Courant Institute), New York, 1953.MATHGoogle Scholar
  2. [2]
    Goldschmidt, B.: Verallgemeinerte analytische Vektoren im n. Thesis (Dissertation B), Martin Luther University, Halle, 1980.Google Scholar
  3. [3]
    Goldschmidt, B.: Existence and representation of solutions of a class of elliptic systems of partial differential equations of first order in the space. Math. Nachr. 108 (1982), 159–166.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Goldschmidt, B.: A Gauchy integral formula for a class of elliptic systems of partial differential equations of first order in the space. Math. Nachr. 108 (1982), 167–178.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Brackx, F., Delanghe, R., Sommen,.F.: Clifford analysis. Pitman, London, 1982.MATHGoogle Scholar
  6. [6]
    Obolashvili, E.: Partial differential equations in Clifford analysis. Addison Wesley Longman, Harlow, 1998.MATHGoogle Scholar
  7. [7]
    Tutschke, W., Yüksel, U.: Interior L p-estimates for functions with integral representations, (submitted to Applicable Analysis).Google Scholar
  8. [8]
    Vekua, I.N.: Generalized analytic functions. Pergamon Press, Oxford, 1962.MATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • W. Tutschke
    • 1
  • U. Yüksel
    • 1
  1. 1.Department of MathematicsTechnical University GrazGrazAustria

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