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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.
List of contents
Preface.- Intro.- The Liouville Operator.- Blaschke Type Products.- Equilibrium Relations and Factorization.- Meromorphic Functions.- Boundary Values.- Uniform Approximations.- Subharmonic Functions.- Weighted Classes of Subharmonic Functions.- Functions of a-Bounded Type in Spectral Theory.- References.- Index.
Summary
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.
