Complex Analysis I: Proceedings of the Special Year Held at the University of Maryland, College Park, 1985-86

ISBN-13: 9783540183563 / Angielski / Miękka / 1987 / 334 str.

Carlos A. Berenstein

Opis

The past several years have witnessed a striking number of important developments in Complex Analysis. One of the characteristics of these developments has been to bridge the gap existing between the theory of functions of one and of several complex variables. The Special Year in Complex Analysis at the University of Maryland, and these proceedings, were conceived as a forum where these new developments could be presented and where specialists in different areas of complex analysis could exchange ideas. These proceedings contain both surveys of different subjects covered during the year as well as many new results and insights. The manuscripts are accessible not only to specialists but to a broader audience. Among the subjects touched upon are Nevanlinna theory in one and several variables, interpolation problems in Cn, estimations and integral representations of the solutions of the Cauchy-Riemann equations, the complex Monge-Ampere equation, geometric problems in complex analysis in Cn, applications of complex analysis to harmonic analysis, partial differential equations.

Spis treści

Bazilevi? theorem and the growth of univalent functions.- Möbius invariant spaces of analytic functions.- Dubinin's symmetrization theorem.- Functions with rapidly decreasing negative fourier coefficients.- On the theory and applications of Qm-normal families of meromorphic functions.- Cauchy Transforms of measures and univalent functions.- Harmonic majorization, harmonic measure and minimal thinness.- Unramified coverings of hyperelliptic Riemann surfaces.- Arcs on which a univalent function has small magnitude.- Uniform and better-than-uniform elliptic approximations on unbounded sets.- Discrete convergence groups.- Representation and duality in weighted frechet spaces of entire functions.- Real zeros of derivatives of meromorphic functions and solutions of differential equations — A survey with problems and conjectures.- Some estimates for harmonic measures.- Hausdorff measures and removable sets.- Approximations of sobolev functions and related topics.- Inequalities for the hyperbolic metric and applications to geometric function theory.- Subharmonic functions with unilateral growth conditions.- Kirwan's conjecture.- On potential approximation of vector fields.- On tangential harmonic approximation and some related problems.- Unbounded quadrature domains.