9.2. Approximation rates and numerical implementation🔗

Theorem 5.10 allows non-band-pass filters and a finite range of coefficient moments. When s>5/2, its second-moment conclusion connects to the Hilbert-valued uniform approximation theorem.

The experiments in Section 8 support the predicted approximation rates on finite test sets and check a closed-form transform independently. They also show a discretization floor. Computing an integral coefficient, sampling a direction and representing that direction with finitely many numbers remain distinct numerical tasks.