On sets of regular growth for functions analytic in an open half plane

We introduce the notion of the set of regular growth for functions analytic in an open half plane. In particular, for a function of completely regular growth in an open half plane, the entire half plane is its set of regular growth. Developed theory is applied to the solution of a problem of Hermitian interpolation in a class of functions of completely regular growth in a half plane with given indicator.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 11, pp. 1486–1501, November, 1994.