Shilov Boundary for Normed Algebras -- BMO-Mappings in the Plane -- Harmonic Forms on Non-Orientable Surfaces -- Periodic Fatou Components and Singularities of the Inverse Function -- On the Normality of Topological Target Manifolds for Riemann-Hilbert Problems -- Geometric Aspects of Generalized Analytic Functions -- The Riemann-Hilbert Boundary Value Problem on a Cut Plane -- On the Logarithm…
Semyon Yakovlevich Khavinson (May 17, 1927 – January 30, 2003) -- S.Ya. Khavinson: Bibliography -- S.Ya. Khavinson: Photos -- The Structural Formulae for Extremal Functions in Hardy Classes on Finite Riemann Surfaces -- Extremal Problems for Nonvanishing Functions in Bergman Spaces -- Generalization of Carathéodory’s Inequality and the Bohr Radius for Multidimensional Power Series -- Remar…
Functional Models for Representations of the Cuntz Algebra -- Relations on Non-commutative Variables and Associated Orthogonal Polynomials -- Functions of Several Variables in the Theory of Finite Linear Structures Part I: Analysis -- Operator Method for Solution of PDEs Based on Their Symmetries -- On the Bessmertny? Class of Homogeneous Positive Holomorphic Functions on a Product of Matrix Ha…
Elementary theory of several complex variables -- Continuation on circular and polycircular domains -- Biholomorphic maps -- Analytic Sets -- Hartogs’ Kugelsatz -- Continuation on Tubular Domains -- Cartan-Thullen Theory -- Local Properties of holomorphic functions.This book gives a comprehensive introduction to complex analysis in several variables. It clearly focusses on special topics in c…
Global Smoothness Preservation, Univariate Case -- Partial Shape Preservation, Univariate Case -- Global Smoothness Preservation, Bivariate Case -- Partial Shape Preservation, Bivariate Case.This monograph examines and develops the Global Smoothness Preservation Property (GSPP) and the Shape Preservation Property (SPP) in the field of interpolation of functions. The study is developed for the u…
The Liouville Operator and Herglotz-Riesz Type Theorems -- Blaschke Type Products -- Equilibrium Relations and Factorizations -- Meromorphic Functions with Summable Tsuji Characteristics -- Boundary Values -- Uniform Approximations -- Subharmonic Functions with Nonnegative Harmonic Majorants -- Weighted Classes of Subharmonic Functions -- Functions of ?-Bounded Type in Spectral Theory of Non-We…
Local Theory -- Complex Manifolds -- Kähler Manifolds -- Vector Bundles -- Applications of Cohomology -- Deformations of Complex Structures.Complex geometry studies (compact) complex manifolds. It discusses algebraic as well as metric aspects. The subject is on the crossroad of algebraic and differential geometry. Recent developments in string theory have made it an highly attractive area, bot…
Differential Calculus in the Complex Plane ? -- Integral Calculus in the Complex Plane ? -- Sequences and Series of Analytic Functions, the Residue Theorem -- Construction of Analytic Functions -- Elliptic Functions -- Elliptic Modular Forms -- Analytic Number Theory -- Solutions to the Exercises.The guiding principle of this presentation of ``Classical Complex Analysis'' is to proceed as quick…