{"paper":{"title":"Operator algebra in the space of images","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"E. Celeghini","submitted_at":"2017-02-09T12:44:12Z","abstract_excerpt":"A consistent description of images on the disk and of their transformations is given as elements of a vector space and of an operators algebra. The vector space of images on the disk $\\mathbb{D}$ is the Hilbert space $L^2(\\mathbb{D})$ that has as a basis the Zernike functions. To construct the operator algebra that transforms the images $L^2(\\mathbb{D})$ must be complemented and the full rigged Hilbert space $RHS(\\mathbb{D})$ considered. Only this rigged Hilbert space allows indeed to write the operators of different cardinality we need to build the ladder operators on the Zernike functions th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03820","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":""},"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"}