The Cramér–Wold theorem states that a Borel probability measure P on R is uniquely determined by its one-dimensional projections. We prove a sharp form of this result, addressing the problem of how… (More)

This article introduces a method for computing upper and lower bounds for the logarithmic capacity of a compact plane set. If the set has the Hölder continuity property, then these bounds converge to… (More)

We develop a least-squares method for computing the analytic capacity of compact plane sets with piecewise-analytic boundary. The method furnishes rigorous upper and lower bounds which converge to… (More)

Let D 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 function f ∈ D to be… (More)

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, with multiple… (More)

The celebrated Kreiss matrix theorem is one of several results relating the norms of the powers of a matrix to its pseudospectra (i.e. the level curves of the norm of the resolvent). But to what… (More)

We treat the problem of characterizing the cyclic vectors in the weighted Dirichlet spaces, extending some of our earlier results in the classical Dirichlet space. The absence of a Carleson-type… (More)

We introduce a method for computing the weighted capacity of a closed plane set. The method automatically yields upper and lower bounds for the capacity, and, for compact sets, these bounds converge… (More)

In this paper we provide conditions under which a distribution is determined by just one randomly chosen projection. Then we apply our results to construct goodnessof-fit tests for the one and… (More)