Fourier-Borel transformation on the hypersurface of any reduced polynomial

الأصل · EN

For any polynomial p on Cⁿ, a variety Vₚ = {z ∈ Cⁿ; p(z)=0 } will be considered. Let Exp(Vₚ) be the space of holomorphic functions of expotential growth on Vₚ. We shall prove that the Fourier-Borel transformation yields an isomorphism of the dual space Exp'(Vₚ) with the space of holomorphic solutions O∂ ₚ(Cⁿ) with respect to the differential operator ∂ p which is obtained by replacing each variable zⱼ with ∂ / ∂ zⱼ in p when p is a reduced polynomial. The result has been shown by Morimoto and by Morimoto-Wada-Fujita only for the case p(z) = z₁² +... + zₙ² + λ(n ≥ 2).