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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
##### Keywords:
holomorphic function; exponential series