Geodesic
Holomorphic functions with positive imaginary part in the future tube
Sbornik. Mathematics, Tome 22 (1974) no. 1, pp. 1-16 
V. S. Vladimirov. Holomorphic functions with positive imaginary part in the future tube. Sbornik. Mathematics, Tome 22 (1974) no. 1, pp. 1-16. http://geodesic.mathdoc.fr/item/SM_1974_22_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Integral representations are established for holomorphic functions in the tubular domain $\tau^+=\mathbf R^4+iV^+$ over the future light cone $V^+$ (i.e. the future tube) of the space of four complex variables. First one gives a description and the corresponding integral representation of holomorphic functions with positive imaginary part in the “generalized unit disk” $ww^*, where $w$ are $2\times2$ complex matrices. Bibliography: 11 titles.

[1] W. Rühl, “Distributions on Minkowski space and their connection with analytic representations of the conformal group”, Comm. Math. Phys., 27 (1972), 53–86 | DOI | MR | Zbl

[2] A. Uhlmann, “Remark on the future tube”, Acta Physica Polonica, 24 (1963), 292–296 | MR

[3] G. E. Shilov, B. L. Gurevich, Integral, mera i proizvodnaya, izd-vo «Nauka», Moskva, 1967

[4] V. S. Vladimirov, Metody teorii funktsii mnogikh kompleksnykh peremennykh, izd-vo «Nauka», Moskva, 1964 | MR

[5] H. J. Bremermann, “On a generalized Dirichlet problem for plurisubharmonic functions and pseudo-convex domains. Characterization of Silov boundaries”, Trans. Amer. Math. Soc., 91 (1959), 246–276 | DOI | MR | Zbl

[6] V. S. Vladimirov, “Preobrazovanie Laplasa obobschennykh funktsii medlennogo rosta”, Sovremennye problemy matematiki, 1, VINITI, Moskva, 1973, 61–84

[7] V. S. Vladimirov, “Obobschenie integralnogo predstavleniya Koshi-Bokhnera”, Izv. AN SSSR, seriya matem., 33 (1969), 90–108 | MR

[8] V. S. Vladimirov, “Golomorfnye funktsii s neotritsatelnoi mnimoi chastyu v trubchatoi oblasti nad konusom”, Matem. sb., 79 (121) (1969), 128–152 | Zbl

[9] R. Nevanlinna, Eindeutige analytische Funktionen, Springer-Verlag, Berlin, 1936 | MR | Zbl

[10] V. S. Vladimirov, Yu. N. Drozhzhinov, “Golomorfnye funktsii v polikruge s neotritsatelnoi mnimoi chastyu”, Matem. zametki, 15:1 (1974), 55–61 | MR | Zbl

[11] S. Bochner, “Group invariance of Cauchy's formula in several variables”, Ann. Math., 45 (1944), 686–707 | DOI | MR | Zbl