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Fourier-Borel transformation on the hypersurface of any reduced polynomial

机译:任何简化多项式的超曲面上的傅立叶-伯雷尔变换

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摘要

For a polynomial p on C~n, the variety V_p = {z ∈ C~n;p(z) = 0} will be considered. Let Exp(V_p) be the space of entire functions of exponential type on V_p, and Exp'(V_p) its dual space. We denote by (partial deriv)_p the differential operator obtained by replacing each variable z_j with partial deriv/partial deriv z_j in p, and by O partial deriv_p(C~n) the space of holomorphic solutions with respect to partial deriv_p. When p is a reduced polynomial, we shall prove that the Fourier-Borel transformation yields a topological linear isomorphism: Exp'(V_p) → O partial deriv_p(C~n). The result has been shown by Morimoto, Wada and Fujita only for the case p(z) = z_1~2 +… + z_n~2 + λ (n ≥ 2).
机译:对于C〜n上的多项式p,将考虑变化量V_p = {z∈C〜n; p(z)= 0}。令Exp(V_p)为V_p上指数型整个函数的空间,而Exp'(V_p)为其对偶空间。我们用(偏导数)_p表示通过用p中的偏导数/偏导数z_j替换每个变量z_j所获得的微分算子,并且用O偏导数(p〜C)表示相对于偏导数的全纯解的空间。当p是一个简化的多项式时,我们将证明傅立叶-伯雷尔变换产生拓扑线性同构:Exp'(V_p)→O偏导数p(C〜n)。仅在p(z)= z_1〜2 +…+ z_n〜2 +λ(n≥2)的情况下,Morimoto,Wada和Fujita证明了结果。

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