The Lagrangian Radon Transform and the Weil representation

Abstract

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 of the operator $\mathcal{R}$ and of the representation of the affine symplectic group in the space of functions on ${\mathbb{R}}^{2n}$.

34 pages, further small changes

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