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On entire functions of \(n\) variables being quasipolynomials in one of the variables. (English) Zbl 0874.32001

Let \(f(z)=\sum^\omega_{j=1} a_je^{\lambda_j z}\) be an entire function of finite order. Here \(\omega<\infty\); \(\lambda_j\in\mathbb{C}\); \(\lambda_j\neq \lambda_i\forall j\neq i\) and the coefficients \(a_j\) are either polynomials or entire functions of degree zero.
The author considers functions \(f(z_1,z)\) on the set \(\mathbb{C}*E\) where \(E\) is a non-pluripolar set in \(\mathbb{C}^{n-1}\) and finds the general form for such class of functions.

MSC:

32A15 Entire functions of several complex variables
30B50 Dirichlet series, exponential series and other series in one complex variable
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