Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics. Their ...

In this note we show that if the areal mean-value theorem holds for a plane domain (subject to a mild regularity condition) for all integrable harmonic functions, then the domain must be a disk. It is ...

This is a preview. Log in through your library . Abstract A continuous function on the complex plane is harmonic if and only if the span of its compositions with entire functions is not dense in the ...

For most of us, harmonic describes a set of musical notes that produce a pleasing sound, or it describes a state of contentment. For Associate Professor of Mathematics Katharine Ott, harmonic ...