Bozhenko O. Interpolation problems in classes of analytic functions of order zero.

In the thesis, interpolation problems f (an) = bn, n = 1, 2…, in the classes of entire functions of zero order and the classes of entire functions of zero proximate order and normal type are considered. Necessary and sufficient conditions for their solvability in terms of canonical products and in terms of the Nevanlinna measure generated by these nodes are obtained. The concept of weakly regular set, which is an analogue of the regular sets in the sense B.Ya. Levin, is introduced. It is shown that weakly regular sets are interpolation sets in classes of entire functions of zero proximate order and normal type. The problem of multiple interpolation in classes of analytic functions of formal zero proximate order and half-formal zero proximate order in the upper half-plane is studied. As for the classes of entire functions, necessary and sufficient conditions for their solvability in terms of Nevanlinna product and in terms of the Nevanlinna measure generated by these nodes are obtained. The concept of weakly regular set in the upper half-plane is introduced. It is shown that such sets are interpolation sets in the class half-formal zero proximate order.