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On a new integral representation of ramified analytic functions. (English. Russian original) Zbl 0844.32006
Russ. Acad. Sci., Izv., Math. 44, No. 3, 645-658 (1995); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 58, No. 3, 211-224 (1994).
The authors present a sequence (depending on an integer parameter) of integral representation formulas for branching (multi-valued) analytic functions of several complex variables. The formulas include as special cases the Cauchy-Fantappiè formula and the formulas of S. G. Gindikin and G. M. Khenkin [Multidimensional complex analysis, Work Collect., Krasnoyarsk 1985, 50-63 (1985; Zbl 0621.32008)]. These new integral representations, viewed as functionals on homology classes, have a useful geometric interpretation.
The authors announced the results in Sov. Math., Dokl. 37, No. 1, 38-41 (1988); translation from Dokl. Akad. Nauk SSSR 298, No. 1, 44-48 (1988; Zbl 0688.32006) and Sov. Math., Dokl. 40, No. 3, 513-516 (1990); translation from Dokl. Akad. Nauk SSSR 309, No. 2, 282-285 (1990; Zbl 0705.32001).

MSC:
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32C30 Integration on analytic sets and spaces, currents
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