Complex geometry and integral representations in the future tube

A. G. Sergeev

Izvestiya. Mathematics , Tome 29 (1987) no. 3, pp. 597-628.

Résumé

The complex geometry of the future tube is studied, and in particular it is proved that the boundary of the future tube cannot be holomorphically straightened along the complex light rays. Using the general Cauchy–Fantappiè representation we derive the Cauchy–Bochner and Jost–Lehmann–Dyson integral representations and representations with Levi and Cauchy barriers for holomorphic functions and for solutions of the $\overline\partial$-equation. Bibliography: 26 titles.

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