Functions of [alpha]-bounded type in the half-plane - 4

This book is related to the theory of functions of a-bounded type in the ha- plane of the complex plane.

I constructed this theory by application of the Li- ville integro-differentiation.

To some extent, it is similar to M.M.Djrbashian's factorization theory of the classes Na of functions of a-bounded type in the disc, as much as the well known results on different classes and spaces of regular functions in the half-plane are similar to those in the disc.

Besides, 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 author's united work with G.M.

Gubreev (Odessa). It gives an application of both a-theories in the disc and in the half-plane 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.

The book is proposed for a wide range of readers. Some of its parts are comprehensible for graduate students, while the book in the whole is intended for young researchers and qualified specialists in the field.