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Eigen functions of the Laplacian of exponential type

  • Mitsuo Morimoto
  • Keiko Fujita

Abstract

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
$$||F|{|_r} = {\rm{sup\{ }}|F(z)|\exp ( - rL*(z));z \in \tilde E\} $$
.

Keywords

Holomorphic Function Entire Function Exponential Type Continuous Linear Mapping Complex Sphere 
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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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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