Grigor A. Barsegian & Heinrich G.W. Begehr 
Topics in Analysis and its Applications [PDF ebook] 

Most topics dealt with here deal with complex analysis of both one and several complex variables. Several contributions come from elasticity theory. Areas covered include the theory of p-adic analysis, mappings of bounded mean oscillations, quasiconformal mappings of Klein surfaces, complex dynamics of inverse functions of rational or transcendental entire functions, the nonlinear Riemann-Hilbert problem for analytic functions with nonsmooth target manifolds, the Carleman-Bers-Vekua system, the logarithmic derivative of meromorphic functions, G-lines, computing the number of points in an arbitrary finite semi-algebraic subset, linear differential operators, explicit solution of first and second order systems in bounded domains degenerating at the boundary, the Cauchy-Pompeiu representation in L2 space, strongly singular operators of Calderon-Zygmund type, quadrature solutions to initial and boundary-value problems, the Dirichlet problem, operator theory, tomography, elastic displacements and stresses, quantum chaos, and periodic wavelets.

Table des matières

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 Logarithmic Derivative of Meromorphic Functions.- Methods for Studying Level Sets of Smooth Enough Functions.- Gamma-Lines of Polynomials and a Problem by Erdös-Herzog-Piranian.- A Method for Studying Oscillations of Nonlinear Differential Equations. Applications to Some Equations in Biology and Economics.- Counting Points of Semi-Algebraic Subsets.- Behaviour at Infinity of Polynomials of Two Variables.- On Some Properties of Degenerate Elliptic Systems of Partial Differential Equations.- Formulas for Derivatives of Solutions of the $$ /bar /partial $$ -Equation in the Ball.- On Some Complex Differential and Singular Integral Operators.- Boundary and Initial Value Problems for Higher Order PDEs in Clifford Analysis.- On Unique Solvability of the Dirichlet Problem for One Class of Properly Elliptic Equations.- Dirichlet Problems with Nonsmooth Boundary.- Dirichlet Problem in the Half-Plane for RO-Varying Weight Functions.- About One Class of Volterra Type Linear Integral Equations with an Interior Fixed Singular or Super-Singular Point.- The Method of Discrete Singularities of Solutions of Singular Integral Equations with Unmoved Singularity.- Localization Operators, Wigner Transforms and Paraproducts.- The Flight of an Aircraft Along a Given Trajectory and Optimal Flight Control.- On Mathematical Problems of Two-Dimensional Tomography.- On a Mixed Problem for a Composite Plane Weakened byarc-Type Cracks.- Solution of the Two-Dimensional Magnetoelastic Lamb Problem.- On an Eigenvalue Problem for the Anisotropic Strip.- On Singular Perturbed Equations of Thin Bodies.- Exactly Solvable Models of Stochastic Quantum Mechanics within the Framework of Langevin-Schroedinger Type Equations.- Generating Functions and Wavelet-Like Decompositions.