Supplementary Material for Representation Equivalent Neural Operators a Framework for Alias free Operator Learning

We show the proof of Proposition 3.7 for a two layer Representation equivalent Neural Operator. The first equality simply follows by the definition of ReNO. A.2 Proof of Remark 3.5 We keep the notation as in Section 3.2. By equation (A.1) we readily obtain T B.1 Fourier layer in FNOs We focus here on the Fourier layer of FNOs, i.e. However, as pointed out in 4, the pointwise activation function applied to a bandlimited input will not necessarily respect the bandwidth.