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On the Divergence of Taylor Series in de Branges-Rovnyak Spaces
Pierre-Olivier Parisé, Thomas Ransford
It is known that there exist functions in certain de Branges--Rovnyak spaces whose Taylor series diverge in norm, even though polynomials are dense in the space. This is often prov…
Holomorphic motions, dimension, area and quasiconformal mappings
Aidan Fuhrer, Thomas Ransford, Malik Younsi
We describe the variation of the Minkowski, packing and Hausdorff dimensions of a set moving under a holomorphic motion, as well as the variation of its area. Our method provides a…
Approximation in the closed unit ball
Javad Mashreghi, Thomas Ransford
In this expository article, we present a number of classic theorems that serve to identify the closure in the sup-norm of various sets of Blaschke products, inner functions and the…
Cantor sets and cyclicity in weighted Dirichlet spaces
Omar El-Fallah, Karim Kellay, Thomas Ransford
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…