3. Representation and reconstruction
This chapter is Section 4 of the manuscript together with Appendix B. The Fourier-slice
identity, read backwards, produces a network from a spectral density
(Theorem 3.1.5); the transpose of the transform is the synthesis operator, and the frame
operator T_\alpha=U_\alpha'U_\alpha is the Riesz map of \mathcal E_\alpha
(Theorem 3.2.7). The Lean statements are for the abstract pair (\mu,\nu) of Appendix H
wherever the manuscript allows it; the Hermite inversion needs the Gaussian input measure.