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 of polyanalytic functions(boundary behaviour，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.
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目录
Introduction Chapter 1 General Theorems on the Asymptotic Behavior of Entire and Meromorphic Functions (A.A.Gol’dberg, B.Ya.Levin, I.V.Ostrovskii) §1. Characteristics of Asymptotic Behavior §2. Relation Between Growth and Decrease §3. Relation Between the Indicator of an Entire Function and Singularities of Its Borel Transform §4. Wiman-Valiron Theory Chapter 2 The Connection Between the Growth of an Entire Function and the Distribution of Its Zeros (B.Ya.Levin, I.V.Ostrovskii) §1. Classical Results §2. Entire Functions of Completely Regular Growth §3. Entire Functions of Exponential Type with Restrictions on the Real Axis §4. Exceptional Sets §5. Two-Term Asymptotics §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 Coefficients Chapter 3 Limit Sets of Entire and Subharmonic Functions (V.S.Azarin) §1. Principal Notations and Theorems §2. Limit Sets and Their Relation to Other Characteristics §3. Applications of Limit Sets §4. Limit Sets as Dynamical Systems Chapter 4 Interpolation by Entire Functions (B.Ya.Levin, V.A.Tkachenko) §1. Newton's Interpolation Series §2. Abel-Gontcharoff Interpolation Series §3. Gelfond’s Moments Problem §4. Lagrange’s Interpolation Series §5. Interpolation Techniques Based on Solving the δ-Problem §6. The Lagrange Interpolation Process in Some Normed Spaces Chapter 5 Distribution of Values of Meromorphic Functions (A.A.Gol’dberg) §1. Main Nevanlinna Theorems. Nevanlinna Deficient Values and Deficient Functions §2. Inverse Problems of Value Distribution Theory §3. The Ahlfors Theory §4. Valiron Deficiencies §5. Exceptional Values in the Sense of Petrenko §6. Asymptotic Curves and Asymptotic Values §7. Julia and Borel Directions. Filling Disks §8. Closeness of a-Points §9. Value Distribution of Derivatives of Meromorphic Functions §10. Value Distribution with Respect to Arguments §11. Value Distribution of Special Classes of Meromorphic Functions §12. Entire Curves Chapter 6 Entire and Meromorphic Solutions of Ordinary Differential Equations (A.E.Eremenko) §1. Nonlinear ADEs with Meromorphic Solutions §2. Linear Differential Equations Chapter 7 Some Applications of the Theory of Entire Functions (I.V.Ostrovskii) §1. Riemann's Boundary Problem with Infinite Index §2. The Arithmetic of Probability Distributions §3. Entire Characteristic and Ridge Functions References
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