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

Dov Aharonov (auth.), Carlos A. Berenstein (eds.)3540183566, 9783540183563

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-Ampère equation, geometric problems in complex analysis in Cn, applications of complex analysis to harmonic analysis, partial differential equations.

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Table of contents :
Bazilevič theorem and the growth of univalent functions….Pages 1-9
Möbius invariant spaces of analytic functions….Pages 10-22
Dubinin’s symmetrization theorem….Pages 23-30
Functions with rapidly decreasing negative fourier coefficients….Pages 31-43
On the theory and applications of Q m -normal families of meromorphic functions….Pages 44-77
Cauchy Transforms of measures and univalent functions….Pages 78-88
Harmonic majorization, harmonic measure and minimal thinness….Pages 89-112
Unramified coverings of hyperelliptic Riemann surfaces….Pages 113-130
Arcs on which a univalent function has small magnitude….Pages 131-148
Uniform and better-than-uniform elliptic approximations on unbounded sets….Pages 149-157
Discrete convergence groups….Pages 158-167
Representation and duality in weighted frechet spaces of entire functions….Pages 168-196
Real zeros of derivatives of meromorphic functions and solutions of differential equations — A survey with problems and conjectures….Pages 197-209
Some estimates for harmonic measures….Pages 210-214
Hausdorff measures and removable sets….Pages 215-222
Approximations of sobolev functions and related topics….Pages 223-234
Inequalities for the hyperbolic metric and applications to geometric function theory….Pages 235-252
Subharmonic functions with unilateral growth conditions….Pages 253-265
Kirwan’s conjecture….Pages 266-271
On potential approximation of vector fields….Pages 272-279
On tangential harmonic approximation and some related problems….Pages 280-286
Unbounded quadrature domains….Pages 287-331