Acta Mathematica Vietnamica
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ENTIRE EIGENFUNCTIONS OF THE LAPLACIAN OF EXPONENTIAL TYPE WITH RESPECT TO THE LIE NORM AND THE DUAL LIE NORM
KEIKO FUJITApp. 81-94
Abstract
We consider entire functions of exponential type with respect to the Lie norm and the dual Lie norm. We characterize them by the growth condition of harmonic components in their double series expansion. Special attention will be paid to the eigenfunctions of the Laplacian.