16 citations · 96 across the 45 of their papers we have counts for
9 papers · 2 filters
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…
Analytic capacity and holomorphic motions
Stamatis Pouliasis, Thomas Ransford, Malik Younsi
We study the behavior of the analytic capacity of a compact set under deformations obtained by families of conformal maps depending holomorphically on the complex parameter. We sho…
Letter to the editor: A short complex-variable proof of the Titchmarsh convolution theorem
Thomas Ransford
The Titchmarsh convolution theorem is a celebrated result about the support of the convolution of two functions. We present a simple proof based on the canonical factorization theo…
Hadamard multipliers on weighted Dirichlet spaces
Javad Mashreghi, Thomas Ransford
The Hadamard product of two power series is obtained by multiplying them coefficientwise. In this paper we characterize those power series that act as Hadamard multipliers on all w…
Covering numbers and schlicht functions
Philippe Drouin, Thomas Ransford
We determine upper and lower bounds for the minimal number of balls of a given radius needed to cover the space of schlicht functions.
Polynomial approximation in weighted Dirichlet spaces
Javad Mashreghi, Thomas Ransford
We give an elementary proof of an analogue of Fejér's theorem in weighted Dirichlet spaces with superharmonic weights. This provides a simple way of seeing that polynomials are den…