Finite order solutions of complex linear differential equations.

Laine, Ilpo; Yang, Ronghua

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

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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 $E x p_{Δ} (\tilde{}; (A, L *))$ 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.