Functions of a-Bounded Type in the Half-Plane

This is a unique book related to the theory of functions of a-bounded type in the half-plane of the complex plane, which is constructed by application of the Liouville integro-differential operator.In addition, the book contains improvements of several results such as the Phragmen-Lindelof Principle and Nevanlinna Factorization in the Half-Plane, and offers a new, equivalent definition of the classical Hardy spaces in the half-plane.The last chapter of the book presents an application of the constructed theory as well as M.M.Djrbashian s theory of Nevanlinna type classes in the disc in the spectral theory of linear operators. This is a solution of a problem repeatedly stated by M.G.Krein and being of special interest for a long time.