Eigen functions of the Laplacian of exponential type

  • Mitsuo Morimoto
  • Keiko Fujita


Let E˜, L(z) the Lie norm on E˜ and L*(z) the dual Lie norm on E˜. We denote by O(E˜) the space of entire functions on E˜ and by Δ z = δ2z 1 2 + δ2z 2 2 + …+ δ2z n+1 2 the complex Laplacian on E˜. Let r > 0. For F ∈ O (E˜) we put
$$||F|{|_r} = {\rm{sup\{ }}|F(z)|\exp ( - rL*(z));z \in \tilde E\} $$


Holomorphic Function Entire Function Exponential Type Continuous Linear Mapping Complex Sphere 
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Copyright information

© Springer-Verlag Tokyo 1997

Authors and Affiliations

  • Mitsuo Morimoto
    • 1
  • Keiko Fujita
    • 2
  1. 1.Department of MathematicsSophia UniversityChiyoda-ku, Tokyo 102Japan
  2. 2.Faculty of EducationSaga UniversitySaga City, Saga 840Japan

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