It is worth noting that circulant matrices are 1-dimensional convolutions with circular padding, and their properties can be extended to doubly-block circulant matrices, which are the 2-dimensional equivalent. The eigendecomposition of doubly-block circulant matrices has been exploited in the context of robustness and stability in deep learning [1, 2, 3].

[1] The Singular Values of Convolutional Layers

[2] Orthogonalizing Convolutional Layers with the Cayley Transform

[3] Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iteration