Supplementary Material for: Convolutional Neural Operators for Robust and Accurate Learning of PDEs. T able of Contents AT echnical Details for Section 2 of main text. 15 A.1

We obtain this result by discarding the high-frequency components, e.g. higher than frequency This proves the statement of the lemma. Appendix A.2 can be adapted to bandlimited Note that the single-channel versions were defined in the main text. We will describe these filters later in the text (see C.1.4) We use the same notation as in Section 2 and Appendix A.2. Hence, they consist of three elementary mappings between spaces of bandlimited functions, i.e., We recall that the convolutional operator appearing in (A.8) takes the form K As in Appendix A.2, the above proofs can be readily adapted We present the proof of a generalization of the universality result of Theorem 3.1. In addition, we will use the following notation in the proof.