On Prime Ideals of the Ring of Differential Operators

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


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):
$$f\left( Z \right)={{\int }_{r}}\left( Z,U \right)\varphi \left( U \right)\overset{\centerdot }{\mathop{U}}\,,\forall Z\in \Re .$$


Differential Operator Harmonic Function Prime Ideal Constant Coefficient Homogeneous Polynomial 
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    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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