Value Distribution Theory and Related Topics: 3 (Advances in Complex Analysis and Its Applications, 3) - Hardcover

Hardcover

ISBN 10: 1402079508 ISBN 13: 9781402079504

Publisher: Springer, 2004

Synopsis

The Nevanlinna theory of value distribution of meromorphic functions, one of the milestones of complex analysis during the last century, was c- ated to extend the classical results concerning the distribution of of entire functions to the more general setting of meromorphic functions. Later on, a similar reasoning has been applied to algebroid functions, subharmonic functions and meromorphic functions on Riemann surfaces as well as to - alytic functions of several complex variables, holomorphic and meromorphic mappings and to the theory of minimal surfaces. Moreover, several appli- tions of the theory have been exploited, including complex differential and functional equations, complex dynamics and Diophantine equations. The main emphasis of this collection is to direct attention to a number of recently developed novel ideas and generalizations that relate to the - velopment of value distribution theory and its applications. In particular, we mean a recent theory that replaces the conventional consideration of counting within a disc by an analysis of their geometric locations. Another such example is presented by the generalizations of the second main theorem to higher dimensional cases by using the jet theory. Moreover, s- ilar ideas apparently may be applied to several related areas as well, such as to partial differential equations and to differential geometry. Indeed, most of these applications go back to the problem of analyzing zeros of certain complex or real functions, meaning in fact to investigate level sets or level surfaces.

About this title

Synopsis

The volume consists of a collection of articles on the value distribution theory and its applications, both in one and several variables. The applied parts include problems related to geometric function theory, linear operators of entire functions, differential and functional equations, uniqueness and interpolation. A unique feature of the book is an extensive research program by the first editor on the Gamma-lines approach to analysis. Some aspects in the book consider Diophantine type equations for meromorphic functions, offering new challenges to complex analysis. Researchers and postgraduate students in complex analysis, differential equations and algebraic geometry would find this book of interest.

Edition details

• Publisher: Springer
• Publication date: 2004
• Language: English
• ISBN 10: 1402079508
• ISBN 13: 9781402079504
• Binding: Hardcover
• Number of pages: 340
• Editor: Barsegian Grigor A., Laine Ilpo, Chung-Chun Yang