Geodesic
Sets of regular growth of functions in the half-plane.~I
Izvestiya. Mathematics , Tome 59 (1995) no. 4, pp. 785-814

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We develop a theory of sets of regular growth of functions that are analytic in the upper half-plane, relative to a given indicator. A function of completely regular growth in the closed half-plane is constructed which has the given indicator and satisfies an additional condition. 
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     author = {K. G. Malyutin},
     title = {Sets of regular growth of functions in the {half-plane.~I}},
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K. G. Malyutin. Sets of regular growth of functions in the half-plane.~I. Izvestiya. Mathematics , Tome 59 (1995) no. 4, pp. 785-814. http://geodesic.mathdoc.fr/item/IM2_1995_59_4_a6/