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math.CV2008
On the Brown--Shields conjecture for cyclicity in the Dirichlet space
Omar El-Fallah, Karim Kellay, Thomas Ransford
Let $\cD$ be the Dirichlet space, namely the space of holomorphic functions on the unit disk whose derivative is square-integrable. We establish a new sufficient condition for a fu…
math.CV2008
Area, capacity and diameter versions of Schwarz's Lemma
Robert B. Burckel, Donald E. Marshall, David Minda +2
The now canonical proof of Schwarz's Lemma appeared in a 1907 paper of Carathéodory, who attributed it to Erhard Schmidt. Since then, Schwarz's Lemma has acquired considerable fame…