Preface List of Contributors Part I Value Distribution of Complex and P-adic Functions Chapter 1 The Second Main Theorem on Generalized Parabolic Manifolds 1.1 Monge-Ampere equations and generalized parabolic manifolds 1.2 Projectivized bundles over Stein manifolds 1.3 Meromorphic global forms 1.4 Analytic and algebraic Plucker Formulas: The classical case 1.5 Plucker’s formulas for generalized parabolic manifolds 1.6 An analogue of the Ahlfors-Stoll estimate 1.7 The second main theorem Chapter 2 P-adic Value Distribution 2.1 Ultrametric analytic functions 2.2 Lazard’s problem and p-adic Nevanlinna theory 2.3 Applications of the Nevanlinna theory Chapter 3 Survey on Meromorphic Functions of Uniqueness 3.1 Introduction and basic results 3.2 Main results and examples Chapter 4 A Survey on Uniqueness Polynomials and Unique Range Sets 4.1 Meromorphic functions sharing points 4.2 Unique range set for meromorphic functions 4.3 Uniqueness polynomials for meromorphic functions Chapter 5 On Petrenko’s Theory of Growth of Meromorphic Functions 5.1 The growth of functions meromorphic in the plane 5.2 The growth of functions meromorphic in the disc 5.3 Separated maximum modulus points of entire and meromorphic functions 5.4 Strong asymptotic values and strong asymptotic spots of entire and meromorphic functions Chapter 6 Linear Operators，Fourier Transforms and the Riemann ξ-function 6.1 The Laguerre-Polya class and the Riemann ξ-function 6.2 Complex zero decreasing sequences and λ-sequences 6.3 The distribution of zeros of Fourier transforms 6.4 Infinite order differential operators and the Riemann ξ-function Chapter 7 Hyperbolic Hypersurfaces of Lower Degrees 7.1 Introduction and main techniques 7.2 Hyperbolic curves 7.3 Hyperbolic surfaces 7.4 Hyperbolic hypersurfaces in P4(C) Chapter 8 Admissible Solutions of Functional Equations of Diophantine Type 8.1 Introduction 8.2 Background and results 8.3 Preliminary lemmas 8.4 Proofs of the results Part II New Applications of the Concept of Differentiability Chapter 9 Recent Developments in Applied Pseudoanalytic Function Theory 9.1 Introduction 9.2 Some definitions and results from pseudoanalytic function theory 9.3 Solutions of second order elliptic equations as real components of complex pseudoanalytic functions 9.4 Complete systems of solutions for second-order equations 9.5 A remark on orthogonal coordinate systems in a plane 9.6 Explicit construction of a generating sequence 9.7 Explicit construction of complete systems of solutions of second-order elliptic equations Chapter 10 Biquaternions for Analytic and Numerical Solution of Equations of Electrodynamics 10.1 Introduction 10.2 Biquaternionic fundamental solutions 10.3 Biquaternionic reformulation of Maxwell’s equations in chiral media 10.4 Completeness of a system of biquaternionic fundamental solutions 10.5 Numerical realization 10.6 Time-dependent Maxwell’s equations for chiral media 10.7 Field equations in a biquaternionic form 10.8 Green function for the operator M 10.9 Inhomogeneous media Chapter 11 Asymptotic Behavior of Subfunctions of Time-Independent Schrodinger Operators 11.1 Introduction 11.2 Subfunctions of the operator Lc 11.3 Phragm′en-Lindel¨of theorem for subfunctions in an n-dimensional cone 11.4 Bilinear series and estimates of the Green’s function of the operator Lq with a radial potential in a cone 11.5 The Blaschke theorem 11.6 Generalization of the Hayman-Azarin theorem 11.7 Subfunctions in tube domains 11.8 Green’s function of the operator Lc 11.9 Eigenfunctions of the Laplace-Beltrami operator on the unit sphere 11.10 Asymptotic behavior of solutions of the equation y"(r)+(n-1)r-1y'(r)-(λr-2+q(r)y(r)=0 Chapter 12 The Bank-Laine Conjecture-a Survey 12.1 Introduction 12.2 Elementary computations and examples 12.3 First results towards the Bank-Laine conjecture 12.4 Solutions with prescribed zero-sequences 12.5 Bank-Laine sequences 12.6 Bank-Laine functions 12.7 The case of a meromorphic A(z) 12.8 Bank-Laine functions in the unit disc Chapter 13 On Complex Solutions to Functional and Non-linear Partial Differential Equations 13.1 Introduction 13.2 The equation f2+g2=1 and related eikonal type equations 13.3 Factorization of partial derivatives and its relation to partial differential equations 13.4 Exact entire solutions of generalized Eikonal and Fermat equations 13.5 Eikonal and Fermat equations with arbitrarily many terms Chapter 14 Clifford Algebras Depending on Parameters and Their Applications to Partial Differential Equations 14.1 Introduction 14.2 Clifford algebras depending on parameters 14.3 Generalized Clifford analysis 14.4 Concluding remarks Chapter 15 Application of Complex Analytic Method to Equations of Mixed (Elliptic-Hyperbolic) Type 15.1 Oblique derivative problem for second order equations of mixed type with parabolic degeneracy 15.2 Oblique derivative problem for second order elliptic equations with parabolic degeneracy 15.3 Oblique derivative problem for degenerate hyperbolic equations of second order 15.4 Oblique derivative problem for second order equations of mixed type with parabolic degeneracy 15.5 Complex analytic method for mixed equations with parabolic degeneracy and some open problems Chapter 16 The Tricomi Problem for Second Order Equations of Mixed Type 16.1 Formulation of the Tricomi problem for mixed equations with degenerate rank 0 16.2 Representation of solutions of Tricomi problem for the degenerate mixed equations 16.3 Existence of solutions of the Tricomi problem for degenerate mixed equations 16.4 Existence of solutions of the Tricomi problem for elliptic equations with parabolic degeneracy Part III Boundary Value Problems Preface of G.Akhalaia and N.Manjavidze Introduction to the Chapters 17-19 Chapter 17 The Problem of Linear Conjugation and Systems of Singular Integral Equations 17.1 Formulation of the problem 17.2 Boundary value problem of linear conjugation with continuous coefficients 17.3 Boundary value problems with piecewise continuous coefficients 17.4 Systems of singular integral equations 17.5 Differentiability of solutions and singular integral equations Chapter 18 Linear Conjugation with Displacement for Analytic Functions 18.1 Introduction and auxiliary propositions 18.2 Linear conjugation with displacement in case of continuous coefficients 18.3 Linear conjugation with displacement in case of piecewise continuous coefficients 18.4 Boundary value problems with displacement containing complex conjugate values of the desired functions Chapter 19 Linear Conjugation with Displacement for Generalized Analytic Functions and Vectors 19.1 Definitions and notations 19.2 Relation between linear conjugation with displacement and generalized analytic functions 19.3 Boundary value problem of linear conjugation with displacement for generalized analytic vectors 19.4 The problem of linear conjugation with displacement for an elliptic system of differential equations 19.5 Differential boundary value problems for generalized analytic vectors Chapter 20 On Boundary Value Problems for Non-Linear Systems of Partial Differential Equations in the Plane 20.1 Introduction 20.2 Dirichlet problem in simply connected domains 20.3 Dirichlet problem in multiply connected domains 20.4 Riemann-Hilbert problem for simply connected domains 20.5 Application of the Schauder principle
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