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Eigen functions of the Laplacian of exponential type

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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 = δ2/δz 1 2 + δ2/δz 2 2 + …+ δ2/δz n+1 2 the complex Laplacian on E˜. Let r > 0. For F ∈ O (E˜) we put

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

.

Dedicated to Professor H. Komatsu on his 60th birthday

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Sophia University, Chiyoda-ku, Tokyo 102, Japan

    Mitsuo Morimoto

  2. Faculty of Education, Saga University, Saga City, Saga 840, Japan

    Keiko Fujita

Authors
  1. Mitsuo Morimoto
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  2. Keiko Fujita
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Editor information

Editors and Affiliations

  1. Centre de Mathematiques, Ecole Polytechnique, 91128, Palaiseau Cedex, France

    Jean-Michel Bony (Professor) (Professor)

  2. Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102, Japan

    Mitsuo Morimoto (Professor) (Professor)

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© 1997 Springer-Verlag Tokyo

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Morimoto, M., Fujita, K. (1997). Eigen functions of the Laplacian of exponential type. In: Bony, JM., Morimoto, M. (eds) New Trends in Microlocal Analysis. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68413-8_3

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  • DOI: https://doi.org/10.1007/978-4-431-68413-8_3

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-68415-2

  • Online ISBN: 978-4-431-68413-8

  • eBook Packages: Springer Book Archive

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