It is known that, for any simply connected proper subdomain Ω of the complex plane and any point ζ in Ω, there are holomorphic functions on Ω that possess ‘universal’ Taylor series expansions about ζ; that is, partial sums ...

A power series that converges on the unit disc D is called universal if its partial sums approx-
imate arbitrary polynomials on arbitrary compacta in CnD that have connected complement.
This paper shows that such series ...

A holomorphic function on a planar domain Ω is said to possess a universal Taylor series about a point ζ of Ω if subsequences of the partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compact ...

Let $ f$ be a holomorphic function on the unit disc, and let $ (S_{n_{k}})$ be a subsequence of its Taylor polynomials about 0. It is shown that the nontangential limit of $ f$ and lim $ _{k\rightarrow \infty }S_{n_{k}}$ ...

It is known that, for any simply connected proper subdomain Ω of the complex plane and any point ζ in Ω, there are holomorphic functions on Ω that possess “universal” Taylor series expansions about ζ; that is, partial sums ...

Suppose that a harmonic function h on a finite cylinder vanishes on the curved part of the boundary. This paper answers a question of Khavinson by showing that h then has a harmonic continuation to the infinite strip bounded ...

This paper describes recent results concerning the notions of differentiability and harmonicity with respect to the ne topology of classical potential theory.

This paper characterizes the subsets E of the unit disc D with the property that the supremum of |f| over E equals the supremum over D for all functions f in the Nevanlinna class.

It is known that corners of interior angle less than π/2 in the boundary of a plane domain are initially stationary for Hele–Shaw flow arising from an arbitrary injection point inside the domain. This paper establishes the ...

Recent work on two-phase free boundary problems has led to the investigation of a new type of quadrature domain for harmonic functions. This paper develops a method of constructing such quadrature domains based on the ...

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 polynomials on arbitrary compacta K outside ...

It is known that, for any simply connected proper subdomain Omega of the complex plane and any point zeta in Omega, there are holomorphic functions on Omega that have "universal" Taylor series expansions about zeta; that ...