Functions of a-Bounded Type in the Half-Plane (Advances in Complex Analysis and Its Applications Book 4)

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. Audience 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 new researchers and qualified specialists in the field 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.

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.

front-matter......Page 1 1The Liouville Operator and Herglotz-Riesz Type Theorems......Page 16 2Blaschke Type Products......Page 36 3Equilibrium Relations and Factorizations......Page 60 4Meromorphic Functions with Summable Tsuji Characteristics......Page 92 5Boundary Values......Page 116 6Uniform Approximations......Page 136 7Subharmonic Functions with Nonnegative Harmonic Majorants......Page 144 8Weighted Classes of Subharmonic Functions......Page 162 9Functions of α-Bounded Type in Spectral Theory of Non-Weak Contractions......Page 174 back-matter......Page 204