国外数学名著系列（续一）（影印版）48：复分析Ⅰ整函数与亚纯函数，多解析函数及其广义性
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作者： （俄罗斯）贡恰尔等编著
出 版 社： 科学出版社
出版时间： 2009-1-1字数：版次： 1页数： 261印刷时间：开本： 16开印次：纸张：I S B N ： 9787030234919包装： 精装内容简介
The first part of the volume contains a comprehensive description of the theory of entire and meromorphic functions of one complex variable and its applications. It includes the fundamental notions,methods and results on the growth of entire functions and the distribution of their zeros, the RolfNevanlinna theory of distribution of values of meromorphic functions including the inverse problem,the theory of completely regular growth, the concept of limit sets for entire and subharmonic functions. The authors describe the applications to the interpolation by entire functions, to entire and meromorphic solutions of ordinary differential equations, to the Riemann boundary problem with an infinite index and to the arithmetic of the convolution semigroup of probability distributions.
Polyanalytic functions form one of the most natural generalizations of analytic functions and are described in Part II. They emerged for the first time in plane elasticity theory where they found important applications(due to Kolossof, Mushelishvili etc.). This contribution contains a detailed review of recent investigations concerning the function-theoretical pecularities ofpolyanalytic functions(boundarybehaviour, value distributions, degeneration, uniqueness etc.).Polyanalytic functions have many points of contact with such fields of analysis as polyharmonic functions, Nevanlinna Theory,meromorphic curves, cluster set theory, functions of several complex variables etc.
目录
COntents
Introduct.ion
Chapter l.General Theorems on the Asymptotic Behavior of Entire and Meromorphic Functions(A.AGol’dberg，BYa.Levin.V.Ostrovskii)
§1.Characteristics of Asymptotic Behavior
§2.Relation Between Growth and Decrease
§3.Relation Between the Indicator of sD Entire Function andSingularities of Its Borel Transform
§4.Wiman-vallrinTheory
Chapter 2.The Connection Between the Growth of an EntireFunction and the Distribution of Its Zeros(B.Ya.Levin.V.Ostrovskii)
§1.Classical Results
§2.Entire Functions of Completely Regular Growth
§3.Entire Functions of Exponential Type with Restrictions on theReal Axis.
§4.Exceptional Sets
§5.Two-Tcrm Asyrnptotics A.A.Gol，dberg，B.Ya.LevinI.V.Ostrovskfi
§6.Approximation of a Subharmonic Function by the Logarithm of the Modulus of an Entire Function
§7.The Relation Between the Growth and Distribution of Zeros and Fourier Coefl~cients
Chapter 3.Limit Sets of Entire and Subharmonic Functions(VS.Azarin).
§1.Principal Notations and Theorems
§2.Limit Sets and Their Dcation to Other Characteristics
§3.Applications of Limit Sets
§4.Limit Sets ss Dynamical Systems
Chapter 4Interpolation by Entire Functions(B.YaLevin，V.A.Tkachenko).
§1.Newton’S Interpolation Series
§2.Abel-conteharoff Interpolation Series
§3.Gelfond，s Moments Problem
§4.Lagrange’8 Interpolation Series
§5.Interpolation Techniques Based on Solving the良Problem
§6.The Lagrange Interpolation Process in Some Normed Spaces
Chapter 5.Distribution of vahues of Meromorphic Functions(AA.Gol，dberg)
§1.Main Nevanlinna Theorems.Nevanlinna Deficient VbLlUes and Deficient Functions
§2.Inverse Problems of Value DistributionTheory
§3.The Ahlfors了heory
§4.valironDeficiencies
§5.Exceptional Values in the Sense of Petrenk0
§6.Asymptotic Curves and Asymptotic Values.
§7.Julia and Borel DirectionsFilling Disks
§8.Closeness of a-Points
§9.Value Distribution of Derivatives of Meromorphic Functions
§10.ValueDistribution with Respect to Arguments
§11.ValueDistribution of Special Classes of Meromorphic Functions
§12.Entire Curves
Chapter 6.Entire and Meromorphic Solutions of Ordinary Differential Equations(A.E.Eremenko)
§1.NonHnear ADEs with Meromorphic Solutions
§2.Linear Differential Equations
Chapter 7.Some Applications of the Theory of Entire Fauctilnm(i.V.Ostrovskii)
§1.Riemann’B Boundary Problem with Infinite Index
§2.The Arithmetic of Probability Distributions
§3.Entire Characteristic and Ridge Functions
References