Fundamental solutions for the Logarithmic Laplacian

The logarithmic Laplacian has been quite popular in recent years and is a prime example of a weakly singular integral operator. In this talk we will describe how to obtain a fundamental solution of the logarithmic Laplacian via renormalization. We will also introduce a Liouville theorem for the logarithmic Laplacian where we classify all functions/distributions that are harmonic with respect to the logarithmic Laplacian.