Harmonic mappings and logharmonic functions occupy a central role in complex analysis and applied mathematics. Harmonic mappings are functions that satisfy Laplace’s equation and are frequently ...

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 ...

Expressions for several conformally invariant pseudometrics on a Riemann surface R are given in terms of three new forms of reduced extremal distance. The pseudometrics are defined by means of various ...

Abstract. We prove gradient estimates for harmonic functions with respect to a d-dimensional unimodal pure-jump Lévy process under some mild assumptions on the density of its Lévy measure. These ...

In the early nineteenth century, the French mathematical physicist Joseph Fourier showed that many mathematical functions can be represented as the weighted sum of a series of sines and cosines of ...