The Schwarz Principle of Reflection. The Logarithmic Potential, Balayage, and Quadrature Domains. Examples of ''Quadrature Identities''. Quadrature Domains: Basic Properties, 1. Quadrature Domains:… Expand

One of the earliest attempts to rigorously prove the solvability of Dirichlet’s boundary value problem was based on seeking the solution in the form of a “potential of double layer”, and this leads… Expand

Generalizing a recent result of H. Hedenmalm for p = 2, a contractive zero-divisor is found in the Bergman space Ap over the unit disk for 1 < p < oo. This is a function G £ Ap with \\G\\P = 1 and a… Expand

Let f be an analytic function in the open unit disk that assumes the values 0 and 1 at least once and an unequal number of rimes in a disk of radius 1 10-5 entered at the origin. We prove that fmust… Expand