For PDE solvers, choose your spectral basis based on the operator's symmetry: real bases for elliptic PDEs, complex bases for time-dependent ones with phase content.
This paper compares two neural operators for solving PDEs: Fourier Neural Operators (FNO) using complex FFT and Hartley Neural Operators (HNO) using real Hartley transforms. Both are iso-parametric but use different spectral bases.