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On the representation of analytic functions of several variables by exponential series. (Russian) Zbl 0771.32004
Let \(D\) be a convex bounded domain in \(\mathbb{C}^ n\), \(0\in D\); let \(f(z)\) be a holomorphic function in a neighborhood of \(\overline D\). The author gives the complete description of the domains \(D\) in which it is possible to expand \(f(z)\) into an exponential series with explicit formulas of the coefficients.

MSC:
32A10 Holomorphic functions of several complex variables
32A05 Power series, series of functions of several complex variables
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