{"paper":{"title":"Harmonic Analysis on Graphs via Isometric Group Embedding: A Canonical Fourier Transform, Shift, and Convolution for Network Signals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"eess.SP","authors_text":"Laurent Bitjoka, Rigobert Fokam Souop","submitted_at":"2026-07-14T23:53:38Z","abstract_excerpt":"Graph signal processing built on the eigenvectors of a Laplacian or adjacency shift inherits three structural compromises: the eigenbasis is fixed only up to rotation within degenerate eigenspaces, the shift is not an isometry, and there is no genuine translation under which filtering is a true convolution. We develop an alternative harmonic analysis that removes all three at once. Given an isometric embedding of a connected graph into a Cayley graph of a finite abelian group, a host on which classical Fourier analysis applies exactly, we define a group-embedding graph Fourier transform from t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13338","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.13338/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}