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 ...

Let X be an age-dependent branching process with lifetime distribution G and age-dependent generating function π (y,s)=∑k=0 ∞ pk(y)sk. We assume that G is right-continuous and G(0+)=G(0)=0. The base ...

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 ...

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 ...