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Entire And Meromorphic Functions, Polyanalytic Functions And Their Generalizations Book Freeshipping

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Complex Analysis1: Entire and Meromorphic Functions, Polyanalytic Functions and Their Generalizations,

by A.A.Gonchar, V.P.Havin and N.K.Nikolski, English, Hardcover, 2009

Product Details

Author A.A.Gonchar, V.P.Havin and N.K.Nikolski

Press Science Press

Isbn 703023491x/9787030234919

Publication Date Jan 2009

Pages 261

Size 16K

Edition First

Cover Hardcover

Language English

Page material gelatine plate paper

Product Description:

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 2. 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.



Chapter 1 .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


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 Coef 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 4 Interpolation 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 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 heory


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



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