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 ...

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 ...

Harmonic univalent mappings are complex functions defined on the open unit disk that satisfy Laplace’s equation and exhibit a one-to-one correspondence between the domain and their image. These ...

In a recent study, mathematicians from Freie Universität Berlin have demonstrated that planar tiling, or tessellation, is much more than a way to create a pretty pattern. Consisting of a surface ...

We study the Dirichlet problem for discrete harmonic functions in unbounded product domains on multidimensional lattices. First we prove some versions of the Phragmén-Lindelöf theorem and use Fourier ...