Journal of the Mathematical Society of Japan

Fourier-Borel transformation on the hypersurface of any reduced polynomial

Atsutaka KOWATA and Masayasu MORIWAKI

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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 p the differential operator obtained by replacing each variable z j with / z j in p , and by O p ( C n ) 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 ( V p ) O 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 ) .

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J. Math. Soc. Japan, Volume 60, Number 1 (2008), 65-73.

First available in Project Euclid: 24 March 2008

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Zentralblatt MATH identifier

Primary: 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Secondary: 32A15: Entire functions 32A45: Hyperfunctions [See also 46F15]

Fourier-Borel transformation entire functions of exponential type holomorphic solutions of PDE reduced polynomial


KOWATA, Atsutaka; MORIWAKI, Masayasu. Fourier-Borel transformation on the hypersurface of any reduced polynomial. J. Math. Soc. Japan 60 (2008), no. 1, 65--73. doi:10.2969/jmsj/06010065.

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