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Explicit representation of structurally finite entire functions. (English) Zbl 1024.32001

The author investigates a new relation for entire functions \(f, f_1, f_2\) which he describes as follows: \(f\) is constructed from \(f_1\) and \(f_2\) by Maskit surgery. The author gives the accurate definition of this relation.
An entire function is called a structurally finite entire function of type \((p,q)\) if it is constructed from \(p\) quadratic blocks of type \(az^2+bz+c\), \(a\neq 0\) and \(q\) exponential blocks of type \(a\exp(bz)+c\), \(ab\neq 0\). The author proves that the set of structurally finite entire functions of type \((p,q)\) coincides with the set of the form \[ \int\limits_0^z(c_pt^p+\dots +c_0)e^{a_q t^q+\dots +a_0} dt+b,\;c_p a_q\neq 0. \]

MSC:

32A15 Entire functions of several complex variables
30D20 Entire functions of one complex variable (general theory)
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References:

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