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Value Distribution Theory and Related Topics

  • Book
  • © 2004

Overview

Editors:
  1. G. Barsegian

    1. National Academy of Sciences of Armenia, Yerevan, Armenia

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  2. I. Laine

    1. University of Joensuu, Joensuu, Finland

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  3. C. C. Yang

    1. Hong Kong University of Science and Technology, Hong Kong, China

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Part of the book series: Advances in Complex Analysis and Its Applications (ACAA, volume 3)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-vii
    Download chapter PDF

  2. Geometric value distribution theory

    1. A New Program of Investigations in Analysis: Gamma-Lines Approaches

      • G. Barsegian
      Pages 1-73

    2. On Level Sets of Quasiconformal Mappings

      • G. A. Sukiasyan
      Pages 75-92

  3. Classical value distribution theory

    1. On the Unintegrated Nevanlinna Fundamental Inequality for Meromorphic Functions of Slow Growth

      • Angel Alonso, Arturo Fernández, Javier Pérez
      Pages 93-104

    2. On Some New Concept of Exceptional Values

      • G. A. Barsegian, C. C. Yang
      Pages 105-116

    3. Maximum Modulus Points, Deviations and Spreads of Meromorphic Functions

      • E. Ciechanowicz, I. I. Marchenko
      Pages 117-129

    4. Composition Theorems, Multiplier Sequences and Complex Zero Decreasing Sequences

      • Thomas Craven, George Csordas
      Pages 131-166

    5. Nevanlinna Theory in an Annulus

      • Risto Korhonen
      Pages 167-179

    6. On Strong Asymptotic Tracts of Functions Holomorphic in a Disk

      • I. I. Marchenko, I. G. Nikolenko
      Pages 181-188

  4. Complex differential and functional equations

    1. A New Trend in Complex Differential Equations: Quasimeromorphic Solutions

      • G. A. Barsegian, A. A. Sarkisian, C. C. Yang
      Pages 189-199

    2. On the Functional Equation P(F)=Q(G)

      • Ha Huy Khoai, Yang C. C.
      Pages 201-207

    3. Value Distribution of the Higher Order Analogues of the First Painlevé Equation

      • Yuzan He
      Pages 209-217

    4. Some Further Results on the Functional Equation P(F)=Q(G)

      • Chung-Chun Yang, Ping Li
      Pages 219-231
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Keywords

About this book

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.

Editors and Affiliations

  • National Academy of Sciences of Armenia, Yerevan, Armenia

    G. Barsegian

  • University of Joensuu, Joensuu, Finland

    I. Laine

  • Hong Kong University of Science and Technology, Hong Kong, China

    C. C. Yang

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