Abstract:
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 ¯∂-equation.
Bibliography: 26 titles.
\Bibitem{Ser86}
\by A.~G.~Sergeev
\paper Complex geometry and integral representations in the future tube
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 3
\pages 597--628
\mathnet{http://mi.mathnet.ru/eng/im1572}
\crossref{https://doi.org/10.1070/IM1987v029n03ABEH000985}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=883161}
\zmath{https://zbmath.org/?q=an:0627.32001|0618.32001}
Linking options:
https://www.mathnet.ru/eng/im1572
https://doi.org/10.1070/IM1987v029n03ABEH000985
https://www.mathnet.ru/eng/im/v50/i6/p1241
This publication is cited in the following 3 articles:
F. V. Hayrapetyan, A. H. Karapetyan, A. A. Karapetyan, “On Weighted Solutions to ¯∂-Equation in the Upper Half-Plane”, J. Contemp. Mathemat. Anal., 56:5 (2021), 270
Lan Ma, “Estimates for the ˉ∂ -equation and zeros of holomorphic functions on the Lie-ball”, Arch. Math, 59:1 (1992), 80
E. M. Chirka, “Introduction to the geometry of CR-manifolds”, Russian Math. Surveys, 46:1 (1991), 95–197
Citation in format AMSBIB
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