Functions of a-Bounded Type in the Half-Plane

1. Front Matter

   Pages i-xvi

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2. The Liouville Operator and Herglotz-Riesz Type Theorems

   Pages 1-20

3. Blaschke Type Products

   Pages 21-44

4. Equilibrium Relations and Factorizations

   Pages 45-76

5. Meromorphic Functions with Summable Tsuji Characteristics

   Pages 77-100

6. Boundary Values

   Pages 101-120

7. Uniform Approximations

   Pages 121-128

8. Subharmonic Functions with Nonnegative Harmonic Majorants

   Pages 129-146

9. Weighted Classes of Subharmonic Functions

   Pages 147-158

10. Functions of α-Bounded Type in Spectral Theory of Non-Weak Contractions

    Pages 159-188

11. Back Matter

    Pages 189-196

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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.

• Meromorphic function
• Nevanlinna theory
• differential operator
• operator
• spectral theory

• Institute of Mathematics, National Academy of Sciences, Armenia

  Armen M. Jerbashian

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