Fourier-Borel transformation on the hypersurface of any reduced polynomial

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概要

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• For a polynomial p on Cn, the variety Vp={z∈Cn;p(z)=0} will be considered. Let Exp(Vp) be the space of entire functions of exponential type on Vp, and Exp′(Vp) its dual space. We denote by ∂p the differential operator obtained by replacing each variable zj with ∂⁄∂zj in p, and by \\mathcal{O}∂p(Cn) the space of holomorphic solutions with respect to ∂p. When p is a reduced polynomial, we shall prove that the Fourier-Borel transformation yields a topological linear isomorphism: Exp′(Vp)→\\mathcal{O}∂p(Cn). The result has been shown by Morimoto, Wada and Fujita only for the case p(z)=z12+···+zn2+λ(n≥2).

• 社団法人 日本数学会の論文
• 2008-01-01

著者

• Moriwaki Masayasu

  Department Of Mathematics Graduate School Of Science Hiroshima University

• KOWATA Atsutaka

  Department of Mathematics Graduate School of Science Hiroshima University

関連論文

• Fourier-Borel transformation on the hypersurface of any reduced polynomial

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