The Schwartz correspondence for the complex motion group on ${\mathbb{C}}^2$

Francesca Astengo, Bianca Di Blasio, Fulvio Ricci

If $(G,K)$ is a Gelfand pair, with $G$ a Lie group of polynomial growth and $K$ a compact subgroup of $G$, the Gelfand spectrum $\Sigma$ of the bi-$K$-invariant algebra $L^1(K\backslash…