"Spatio-spectral limiting on powers of three-cycles"Lakey, JosephDiscrete tori are N-th Cartesian powers of the integers modulo m, for some m, thought of as vertices of graphs whose adjacencies encode the Cartesian product structure. Space-limiting refers to truncation to a symmetric path neighborhood of the zero element and spectrum limiting in this case refers to corresponding truncation in the isomorphic Fourier domain. Composition spatio-spectral limiting operators are analogues of classical time and band limiting operators. Certain adjacency-invariant spaces of vectors defined on discrete tori are shown to have bases consisting of Fourier transforms of eigenvectors of spatio-spectral limiting operators. We show that when m=3, all eigenvectors of spatio-spectral limiting arise in this way. |
| http://univie.ac.at/projektservice-mathematik/e/talks/Lakey_2021-07_iccha_short_jdl.pdf |
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