On the finite representation of group equivariant operators via permutant measures

The study of G-equivariant operators is of great interest to explain and understand the architecture of neural networks. In this paper we show that each linear G-equivariant operator can be produced by a suitable permutant measure, provided that the group G transitively acts on a finite signal domain X. This result makes available a new method to build linear G-equivariant operators in the finite setting.