A type of lower estimate for entire functions of finite order, and some applications

This paper describes some classes of entire functions of finite order that admit natural estimates outside a system of pairwise disjoint disks with centers at the zeros. The Hermite interpolation problem is solved under weaker conditions than were previously used, for the class of functions of finite type and for classes of functions with indicator not exceeding a given one. In a number of spaces of holomorphic functions we describe, completely or partially, the invariant subspaces in which the root vectors of the differentiation operator form a basis.
Bibliography: 41 titles.