Acta Mathematica

, Volume 182, Issue 2, pp 283–300 | Cite as

Fundamental solutions of real homogeneous cubic operators of principal type in three dimensions

  • Peter Wagner


Fundamental Solution Principal Type 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Atiyah, M. F., Bott, R. &Gårding, L., Lacunas for hyperbolic differential operators with constant coefficients, I.Acta Math., 124 (1970), 109–189.MathSciNetGoogle Scholar
  2. [2]
    Borovikov, V. A., Fundamental solutions of linear partial differential equations with constant coefficients.Trudy Moskov. Mat. Obshch., 8 (1959), 199–257 (Russian); English translation inAmer. Math. Soc. Transl. Ser. 2, 25 (1963), 11–66.MATHMathSciNetGoogle Scholar
  3. [3]
    Brieskorn, E. &Knörrer, H.,Ebene algebraische Kurven. Birkhäuser, Basel, 1981; English translation:Plane Algebraic Curves. Birkhäuser, Basel, 1986.Google Scholar
  4. [4]
    Burau, W.,Algebraische Kurven und Flächen, Vol. I. de Gruyter, Berlin, 1962.Google Scholar
  5. [5]
    Fredholm, I., Sur les équations de l'équilibre d'un corps solide élastique.Acta Math., 23 (1900), 1–42.Google Scholar
  6. [6]
    Gårding, L.,Mathematics and Mathematicians: Mathematics in Sweden before 1950. Amer. Math. Soc., Providence, RI, 1998.Google Scholar
  7. [7]
    Gel'fand, I. M. &Shilov, G. E.,Generalized Functions, I:Properties and Operations. Academic Press, New York, 1964.Google Scholar
  8. [8]
    Gradshteyn, I. S. &Ryzhik, I. M.,Tables of Integrals, Series, and Products. Academic Press, New York-London-Toronto, 1980.Google Scholar
  9. [9]
    Griffiths, P. &Harris, J.,Principles of Algebraic Geometry. Wiley, New York, 1978.Google Scholar
  10. [10]
    Gröbner, W. &Hofreiter, N.,Integraltafel, Teil 2: Bestimmte Integrale, 5th edition. Springer-Verlag, Vienna, 1973.Google Scholar
  11. [11]
    Hörmander, L.,The Analysis of Linear Partial Differential Operators, Vol. I. Grundlehren Math. Wiss., 256. Springer-Verlag, Berlin, 1983.Google Scholar
  12. [12]
    Hörmander, L.,The Analysis of Linear Partial Differential Operators, Vol. II. Grundlehren Math. Wiss., 257. Springer-Verlag, Berlin, 1983.Google Scholar
  13. [13]
    Horváth, J.,Topological Vector Spaces and Distributions, Vol. I. Addison-Wesley, Reading, MA, 1966.Google Scholar
  14. [14]
    Kaplansky, I.,Fields and Rings, 2nd edition. Univ. Chicago Press, Chicago, 1972.Google Scholar
  15. [15]
    Meise, R., Taylor, B. A. &Vogt, D., Continuous linear right inverses for partial differential operators of order 2 and fundamental solutions in half spaces.Manuscripta Math., 90 (1996), 449–464.MathSciNetGoogle Scholar
  16. [16]
    Ortner, N. &Wagner, P., On the fundamental solution of the operator of dynamic linear thermoelasticity.J. Math. Anal. Appl., 170 (1992), 524–550.CrossRefMathSciNetGoogle Scholar
  17. [17]
    Prasolov, V. &Solovyev, Y.,Elliptic Functions and Elliptic Integrals. Amer. Math. Soc., Providence, RI, 1997.Google Scholar
  18. [18]
    Schwartz, L.,Théorie des distributions, nouvelle édition. Hermann, Paris, 1966.Google Scholar
  19. [19]
    Wagner, P., A fundamental solution of N. Zeilon's operator. To appear inMath. Scand. Google Scholar
  20. [20]
    Zeilon, N., Sur les intégrales fondamentales des équations à charactéristique réelle de la Physique Mathématique.Ark. Mat. Astr. Fys., 9:18 (1913–14), 1–70.Google Scholar

Copyright information

© Institut Mittag-Leffler 1999

Authors and Affiliations

  • Peter Wagner
    • 1
  1. 1.Institut für Mathematik und GeometrieUniversität InnsbruckInnsbruckAustria

Personalised recommendations