3. The Gaussian-weighted ridgelet transform🔗

We construct the input and direction measures, the partial Fourier transform, and the coefficient operator before proving Plancherel and injectivity. Every supporting statement and proof needed below is given here, before its use. The coordinates are c=-b, as in the Lean declarations.

1. 3.1. Gaussian input and homogeneous direction measures
2. 3.2. Filters, the ridgelet transform, and the Fourier slice
3. 3.3. Partial Fourier transformation and the coefficient operator
4. 3.4. The Hilbert space E-alpha
5. 3.5. Plancherel identity, closed range, and injectivity
6. 3.6. Examples of analysis filters