  Topological Signal Processing (TSP) utilizes simplicial complexes to model
structures with higher order than vertices and edges. In this paper, we study
the transferability of TSP via a generalized higher-order version of graphon,
known as complexon. We recall the notion of a complexon as the limit of a
simplicial complex sequence [1]. Inspired by the graphon shift operator and
message-passing neural network, we construct a marginal complexon and complexon
shift operator (CSO) according to components of all possible dimensions from
the complexon. We investigate the CSO's eigenvalues and eigenvectors and relate
them to a new family of weighted adjacency matrices. We prove that when a
simplicial complex signal sequence converges to a complexon signal, the
eigenvalues, eigenspaces, and Fourier transform of the corresponding CSOs
converge to that of the limit complexon signal. This conclusion is further
verified by two numerical experiments. These results hint at learning
transferability on large simplicial complexes or simplicial complex sequences,
which generalize the graphon signal processing framework.
