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On construction of entire and quasi-entire functions of finite order uniformly decreasing in the angular domain. I. (English. Russian original) Zbl 0890.30018

J. Contemp. Math. Anal., Armen. Acad. Sci. 31, No. 6, 11-25 (1996); translation from Izv. Akad. Nauk Armen., Mat. 31, No. 6, 15-30 (1996).
The author constructs functions \[ f(z)= a_0+ \sum^\infty_{n=1} a_n z^{\alpha_n}, \;0<\alpha_1 <\alpha_2 <\dots (\arg z=0 \text{ for } z>0) \] of order \(\rho\) and normal type which very quickly decrease in the angle \(|\arg z|\leq{\pi \over \rho'}\), \(\rho' \geq \rho\). The formulation of the main result needs refinement. This result and one of Arakelyan (1966) complement each other.

MSC:

30D15 Special classes of entire functions of one complex variable and growth estimates
30A10 Inequalities in the complex plane
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