Fourier-Borel transformation on the hypersurface of any reduced polynomial
KOWATA, Atsutaka ; MORIWAKI, Masayasu
J. Math. Soc. Japan, Tome 60 (2008) no. 1, p. 65-73 / Harvested from Project Euclid
For a polynomial $p$ on $\mathbf{C}^{n}$ , the variety $ V_{p} = \{ z \in \mathbf{C}^{n} ; p(z)=0 \} $ will be considered. Let $\mathrm{Exp}(V_{p})$ be the space of entire functions of exponential type on $V_{p}$ , and $\mathrm{Exp}^{\prime}(V_{p})$ its dual space. We denote by $\partial p$ the differential operator obtained by replacing each variable $z_{j}$ with $\partial / \partial z_{j}$ in $p$ , and by $\mathcal{O}_{\partial p}(\mathbf{C}^{n})$ the space of holomorphic solutions with respect to $\partial p$ . When $p$ is a reduced polynomial, we shall prove that the Fourier-Borel transformation yields a topological linear isomorphism: $\mathrm{Exp}^{\prime}(V_{p}) \to \mathcal{O}_{\partial p}(\mathbf{C}^{n})$ . The result has been shown by Morimoto, Wada and Fujita only for the case $p(z) = z_{1}^{2} + \cdots + z_{n}^{2} + \lambda \, (n \geq 2)$ .
Publié le : 2008-01-15
Classification:  Fourier-Borel transformation,  entire functions of exponential type,  holomorphic solutions of PDE,  reduced polynomial,  42B10,  32A15,  32A45
@article{1206367955,
     author = {KOWATA, Atsutaka and MORIWAKI, Masayasu},
     title = {Fourier-Borel transformation on the hypersurface of any reduced polynomial},
     journal = {J. Math. Soc. Japan},
     volume = {60},
     number = {1},
     year = {2008},
     pages = { 65-73},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1206367955}
}
KOWATA, Atsutaka; MORIWAKI, Masayasu. Fourier-Borel transformation on the hypersurface of any reduced polynomial. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp.  65-73. http://gdmltest.u-ga.fr/item/1206367955/