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On Prime Ideals of the Ring of Differential Operators

  • Hung-Hsi Wu
Part of the The University Series in Mathematics book series (USMA)

Abstract

As everybody knows,the fundamental facts about the theory of harmonic functions in the classical domain of several complex variables consist of the following.Let R be a classical domain,Γ its characteristic manifold,and △ the Laplace-Beltrami operator of R.If △f=0, fC (R) is said to be harmonic.Suppose f stands for the harmonic function whose continuous boundary value is φ on Г.Then in R,f is given by the following Poisson integral (see Ref.3):
$$f\left( Z \right)={{\int }_{r}}\left( Z,U \right)\varphi \left( U \right)\overset{\centerdot }{\mathop{U}}\,,\forall Z\in \Re .$$
(7.1)

Keywords

Differential Operator Harmonic Function Prime Ideal Constant Coefficient Homogeneous Polynomial 
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References

  1. 1.
    A. Erdelyi, et al, Higher Transcendental Functions,New York (1953).Google Scholar
  2. 2.
    L.-K. Hua, Harmonic Analysis of Functions of Several Complex Variables in the Classical Domain, Science Press, Beijing (1958) (in Chinese); American Mathematical Society, Providence, RI (1968).Google Scholar
  3. 3.
    L.-K. Hua and L.-H. Look, Theory of harmonic function in the classical domain. I, Acta Math. Sinica 8, 531–547 (1958); Sci. Sinica 9, 1031–1094 (1958) (in English).MathSciNetGoogle Scholar
  4. 4.
    H. Maass, Zur Theorie der Harmonischen Formen, Math. Ann., 137, 142–149 (1959).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Hung-Hsi Wu
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

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