Eigen functions of the Laplacian of exponential type

Mitsuo Morimoto and Keiko Fujita
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Mitsuo Morimoto: Sophia University, Department of Mathematics
Keiko Fujita: Saga University, Faculty of Education

A chapter in New Trends in Microlocal Analysis, 1997, pp 39-58 from Springer

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

Keywords: Holomorphic Function; Entire Function; Exponential Type; Continuous Linear Mapping; Complex Sphere (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1007/978-4-431-68413-8_3

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