الصفحة 1
الصفحة 1
Value-Distribution of L-Functions
This book presents recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. In this book the author proves universality for polynomial Euler products.is written in a narrative and reader friendly language. The author gives many examples, presents main hypotheses and problems in the recent theory of universality. There is a large bibliography of 372 entries. The book is recommended for everybody wanting to see the current panorama of the universality theory.
Value Distribution Theory Related to Number Theory
The subject of the book is Diophantine approximation and Nevanlinna theory. Not only does the text provide new results and directions, it also challenges open problems and collects latest research activities on these subjects made by the authors over the past eight years. Some of the significant findings are the proof of the Green-Griffiths conjecture by using meromorphic connections and Jacobian sections, and a generalized abc-conjecture.
The Painlevé Handbook
This book introduces the reader to methods allowing one to build explicit solutions to these equations. A prerequisite task is to investigate whether the chances of success are high or low, and this can be achieved without any a priori knowledge of the solutions, with a powerful algorithm presented in detail called the Painlevé test. If the equation under study passes the Painlevé test, the equation is presumed integrable. If on the contrary the test fails, the system is nonintegrable or even chaotic, but it may still be possible to find solutions.
Operator Theory in Inner Product Spaces
Contains contributions written by participants of the 4th Workshop on Operator Theory in Krein Spaces and Applications, which was held at the TU Berlin, Germany, December 17 to 19, 2004. The workshop covered topics from spectral, perturbation and extension theory of linear operators and relations in inner product spaces, including spectral analysis of differential operators, the theory of generalized Nevanlinna functions and related classes of functions, spectral theory of matrix polynomials, and problems from scattering theory.
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.
