6 citations · 8 across the 4 of their papers we have counts for
7 papers
A strong form of Plessner's theorem
Stephen J. Gardiner, Myrto Manolaki
Let be a holomorphic, or even meromorphic, function on the unit disc. Plessner's theorem then says that, for almost every boundary point , either (i) has a finite nontan…
Isoperimetric inequalities for Bergman analytic content
Stephen J. Gardiner, Marius Ghergu, Tomas Sjödin
The Bergman -analytic content () of a planar domain measures the -distance between and the Bergman space of holomorphic…
Harmonic functions which vanish on coaxial cylinders
Stephen J. Gardiner, Hermann Render
It was recently established that a function which is harmonic on an infinite cylinder and vanishes on the boundary necessarily extends to an entire harmonic function. This paper co…
Analytic content and the isoperimetric inequality in higher dimensions
Stephen J. Gardiner, Marius Ghergu, Tomas Sjödin
This paper establishes a conjecture of Gustafsson and Khavinson, which relates the analytic content of a smoothly bounded domain in to the classical isoperimetric…
Boundary behaviour of Dirichlet series with applications to universal series
Stephen J. Gardiner, Myrto Manolaki
This paper establishes connections between the boundary behaviour of functions representable as absolutely convergent Dirichlet series in a half-plane and the convergence propertie…
A convergence theorem for harmonic measures with applications to Taylor series
Stephen J. Gardiner, Myrto Manolaki
Let be a holomorphic function on the unit disc, and be a subsequence of its Taylor polynomials about . It is shown that the nontangential limit of and lim$…
Universal Taylor series, conformal mappings and boundary behaviour
Stephen J. Gardiner
A holomorphic function f on a simply connected domain Ω is said to possess a universal Taylor series about a point in Ω if the partial sums of that series approximate arbitrary pol…