The Lagrangian Radon Transform and the Weil representation

Giuseppe Marmo, Peter W. Michor, Yuri Neretin

We consider the operator $\mathcal{R}$, which sends a function on ${\mathbb{R}}^{2n}$ to its integrals over all affine Lagrangian subspaces in ${\mathbb{R}}^{2n}$. We discuss properties o…