Conical Fourier-Borel transformations for harmonic functionals on the Lie ball

Mitsuo Morimoto; Keiko Fujita

ArticleOriginal scientific text

Title

Conical Fourier-Borel transformations for harmonic functionals on the Lie ball

Authors ¹, ¹

Affiliations

Department of Mathematics, Sophia University, 7-1, Kioicho, Chiyoda-ku, Tokyo, 102 Japan

Abstract

Let L(z) be the Lie norm on

\tilde{} = ℂ^{n + 1}

and L*(z) the dual Lie norm. We denote by

_Δ (\tilde{B} (R))

the space of complex harmonic functions on the open Lie ball

\tilde{B} (R)

and by

E x p_{Δ} (\tilde{}; (A, L \cdot))

the space of entire harmonic functions of exponential type (A,L*). A continuous linear functional on these spaces will be called a harmonic functional or an entire harmonic functional. We shall study the conical Fourier-Borel transformations on the spaces of harmonic functionals or entire harmonic functionals.

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Title

Conical Fourier-Borel transformations for harmonic functionals on the Lie ball

Affiliations

Abstract

Bibliography