Matematikseminarium: Generalised harmonic functions

Föreläsare: Markus Klintborg, Högskolan i Borås

Sammanfattning: The idea of a generalised harmonic function is a loosely defined concept that has been applied across many different contexts. It commonly refers to a function that satisfies an equation which, in one way or another, resembles that of Laplace. Classical examples include the Helmholtz equation, the biharmonic equation, and many others arising in physical and engineering applications. 

We will elaborate on this notion and examine a few examples arising in the harmonic analysis of complex such functions, especially in relation to their decomposition and construction. This will also reveal why certain symmetry constraints must be imposed on the underlying equations in order to make the analysis tractable, and leads naturally to a framework that raises new questions about the relationships between these functions and the equations they satisfy.