Topics in Analysis and Its Applications

ISBN-13: 9781402020636 / Angielski / Miękka / 2004 / 469 str.

Grigor Barsegian; Heinrich G. W. Begehr

Opis

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.

Spis treści

Preface. Shilov boundary for normed algebras; A. Escassut, N.M. Netti. BMO-mappings in the plane; C.A. Cazacu, V. Stanciu. Harmonic forms on non-orientable surfaces; A. Alonso, A. Fernández, J. Pérez. Periodic Fatou components and singularities of the inverse function; W. Bergweiler. On the normality of topological target manifolds for Riemann-Hilbert problems; E. Wegert, B. Semmler. Geometric aspects of generalized analytic functions; G. Giorgadze. The Riemann-Hilbert boundary value problem on a cut plane; N. Manjavidze. On the logarithmic derivative of meromorphic functions; A.A. Mokhon'ko, A.Z. Mokhon'ko. Methods for studying level sets of smooth enough functions; G.A. Barsegian, G.A. Sukiasyan. Gamma-lines of polynomials and a problem by Erdös-Herzog-Piranian.G.A. Barsegian. A method for studying oscillations of non-linear differential equations. Applications to some equations in biology and economics; K. Barseghyan, G.A. Barsegian. Counting points of semi-algebraic subsets; T. Aliashvili. Behaviour at infinity of polynomials of two variables; H.G. Ghazaryan, V.N. Margaryan. On some properties of degenerate elliptic systems of partial differential eqations; A. Dzhuraev. Formulas for derivatives of solutions of the DBAR-equation in the ball; A.I. Petrosyan. On some complex differential and singular integral operators; H. Begehr, A. Dzhuraev. Boundary and initial value problems for higher order PDEs in Clifford analysis; E. Obolashvili. On unique solvability of the Dirichlet problem for one class of properly elliptic equations; A.O. Babayan. Dirichlet problems in the half plane for RO-varying weight functions; H. Hairapetian. About one class of Volterra type linear integral equations with an interior fixed singular or super-singular point; N.Rajabov. The method of discrete singularities of solutions of singular integral equations with unmoved singularity; A. Sahakyan. Localization operators, Wigner transforms and paraproducts; M.W. Wong. The flight of an aircraft along a given trajectory and optimal flight control; N.E. Tovmasyan. On mathematical problems of two-dimensional tomography; A. Vagarshakyan. On a mixed problem for a composite plane weakened by arc-type cracks; V.N. Hakobyan, L.L. Dashtoyan. Solution of the two-dimensional magnetoelastic Lamb problem; G.Y. Baghdasaryan, Z.N. Danoyan, M.A. Mikilyan. On an eigenvalue problem for the anisotropic strip; M. Aghalovyan. On singular perturbed equations of thin bodies; L. Aghalovyan. Exactly solvable models of stochastic quantum mechanics within the framework of Langevin-Schrödinger type equations; A.S. Gevorkyan. Generating functions and wavelet-like decompositions; A. Nersessian. Index of Names. Index of Subjects.