Ebook: Topics in Analysis and its Applications

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.

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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.

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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.
Content:
Front Matter....Pages i-xiii
Shilov Boundary for Normed Algebras....Pages 1-10
Harmonic Forms on Non-Orientable Surfaces....Pages 11-30
Periodic Fatou Components and Singularities of the Inverse Function....Pages 31-46
On the Normality of Topological Target Manifolds for Riemann-Hilbert Problems....Pages 47-59
Geometric Aspects of Generalized Analytic Functions....Pages 61-68
The Riemann-Hilbert Boundary Value Problem on a Cut Plane....Pages 69-81
On the Logarithmic Derivative of Meromorphic Functions....Pages 83-90
Methods for Studying Level Sets of Smooth Enough Functions....Pages 91-103
Gamma-Lines of Polynomials and a Problem by Erd?s-Herzog-Piranian....Pages 105-118
A Method for Studying Oscillations of Nonlinear Differential Equations. Applications to Some Equations in Biology and Economics....Pages 119-122
Counting Points of Semi-Algebraic Subsets....Pages 123-148
Behaviour at Infinity of Polynomials of Two Variables....Pages 149-161
On Some Properties of Degenerate Elliptic Systems of Partial Differential Equations....Pages 163-190
On Some Complex Differential and Singular Integral Operators....Pages 191-227
Boundary and Initial Value Problems for Higher Order PDEs in Clifford Analysis....Pages 229-233
On Unique Solvability of the Dirichlet Problem for One Class of Properly Elliptic Equations....Pages 235-269
Dirichlet Problems with Nonsmooth Boundary....Pages 271-286
Dirichlet Problem in the Half-Plane for RO-Varying Weight Functions....Pages 287-293
About One Class of Volterra Type Linear Integral Equations with an Interior Fixed Singular or Super-Singular Point....Pages 295-309
The Method of Discrete Singularities of Solutions of Singular Integral Equations with Unmoved Singularity....Pages 311-316
Localization Operators, Wigner Transforms and Paraproducts....Pages 317-326
The Flight of an Aircraft Along a Given Trajectory and Optimal Flight Control....Pages 327-332
On Mathematical Problems of Two-Dimensional Tomography....Pages 333-346
On a Mixed Problem for a Composite Plane Weakened by arc-Type Cracks....Pages 347-364
Solution of the Two-Dimensional Magnetoelastic Lamb Problem....Pages 365-375
On an Eigenvalue Problem for the Anisotropic Strip....Pages 377-383
On Singular Perturbed Equations of Thin Bodies....Pages 385-396
Exactly Solvable Models of Stochastic Quantum Mechanics within the Framework of Langevin-Schroedinger Type Equations....Pages 397-401
Generating Functions and Wavelet-Like Decompositions....Pages 403-413
Back Matter....Pages 415-442
....Pages 443-451