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On preservation of completely regular growth by a differential operator of infinite order. (Russian) Zbl 0662.47024
In the paper the differential operator $a(D)=\sum^{\infty}_{k=0}\frac{a^{(k)}(0)}{k!}\frac{d^ k}{dz^ k}$ of infinite order is considered with the characteristic function $$a(z)=\sum^{\infty}_{k=0}a_ kz^ k$$. The main result of this paper is given by a theorem where under some conditions the preservation of the completely regular growth by this operator is proved.

##### MSC:
 4.7e+06 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)