What would be the best way to implement support differentiation of a SubSpace

[vincentcp]

At this moment

julia> S = ApproxFunBase.SubSpace(Fourier(), 1:10);

julia> Derivative(S)
DerivativeWrapper : Fourier(【0.0,6.283185307179586❫)|1:10 → SinSpace(【0.0,6.283185307179586❫)⊕CosSpace(【0.0,6.283185307179586❫)
 0.0  0.0  -1.0  0.0   0.0  0.0   0.0  0.0   0.0  0.0
 0.0  0.0   0.0  0.0   0.0  0.0   0.0  0.0   0.0  0.0
 0.0  0.0   0.0  0.0  -2.0  0.0   0.0  0.0   0.0  0.0
 0.0  1.0   0.0  0.0   0.0  0.0   0.0  0.0   0.0  0.0
 0.0  0.0   0.0  0.0   0.0  0.0  -3.0  0.0   0.0  0.0
 0.0  0.0   0.0  2.0   0.0  0.0   0.0  0.0   0.0  0.0
 0.0  0.0   0.0  0.0   0.0  0.0   0.0  0.0  -4.0  0.0
 0.0  0.0   0.0  0.0   0.0  3.0   0.0  0.0   0.0  0.0
 0.0  0.0   0.0  0.0   0.0  0.0   0.0  0.0   0.0  0.0
 0.0  0.0   0.0  0.0   0.0  0.0   0.0  4.0   0.0  0.0

while the first dimension could be finite.

Where would be the best place to interrupt the ApproxFunBase flow to create an Operator that is finite in both dimensions?

[dlfivefifty]

You would want to override Derivative(::SubSpace). You can infer the finite-ness from the bandwidths of the full operator.