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Integral formulas on projective space and the radon transform of Gindikin-Henkin-Polyakov.

Bo Berndtsson (1988)

Publicacions Matemàtiques

We construct a variant of Koppelman's formula for (0,q)-forms with values in a line bundle, O(l), on projective space. The formula is then applied to a study of a Radon transform for (0,q)-forms, introduced by Gindikin-Henkin-Polyakov. Our presentation follows along the basic lines of Henkin-Polyakov [3], with some simplifications.

Integral representations for solutions of exponential Gauß-Manin systems

Marco Hien, Céline Roucairol (2008)

Bulletin de la Société Mathématique de France

Let f , g : U 𝔸 1 be two regular functions from the smooth affine complex variety U to the affine line. The associated exponential Gauß-Manin systems on the affine line are defined to be the cohomology sheaves of the direct image of the exponential differential system 𝒪 U e g with respect to f . We prove that its holomorphic solutions admit representations in terms of period integrals over topological chains with possibly closed support and with rapid decay condition.

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