16 citations · 96 across the 45 of their papers we have counts for
28 papers · 1 filter
A holomorphic motion with non-subharmonic Hausdorff dimension
Thomas Ransford, Malik Younsi
We present an example of a holomorphic motion of a Cantor set for which neither the Hausdorff dimension $\dimH(A_λ)$ nor the lower Minkowski dimension $\dimMl(A_λ)$…
A Schwarz-Jack lemma, circularly symmetric domains and numerical ranges
Javad Mashreghi, Annika Moucha, Ryan O'Loughlin +2
We prove a Schwarz-Jack lemma for holomorphic functions on the unit disk with the property that their maximum modulus on each circle about the origin is attained at a point on the…
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…
Weakly multiplicative distributions and weighted Dirichlet spaces
Javad Mashreghi, Thomas Ransford
We show that if is a compactly supported distribution on the complex plane such that, for every pair of entire functions , \[ \langle u,f\overline{g}\rangle=\langle u,f\ra…
On the decay of singular inner functions
Thomas Ransford
It is known that, if is a non-constant, singular inner function defined on the unit disk, then as . We show that the convergence may be…