Prefer a chat interface with context about you and your work?
Distributions that are convolvable with generalized Poisson kernel of solvable extensions of homogeneous Lie groups
In this paper, we characterize the class of distributions on a homogeneous Lie group $\mathfrak N$ that can be extended via Poisson integration to a solvable one-dimensional extension $\mathfrak S$ of $\mathfrak N$. To do so, we introduce the $\mathcal S'$-convolution on $\mathfrak N$ and show that the set of …