{"paper":{"title":"Two-Dimensional Adaptive Fourier Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Tao Qian","submitted_at":"2014-06-09T06:52:24Z","abstract_excerpt":"One-dimensional adaptive Fourier decomposition, abbreviated as 1-D AFD, or AFD, is an adaptive representation of a physically realizable signal into a linear combination of parameterized Szeg\\\"o and higher order Szeg\\\"o kernels of the context. In the present paper we study multi-dimensional AFDs based on multivariate complex Hardy spaces theory. We proceed with two approaches of which one uses Product-TM Systems; and the other uses Product-Szeg\\\"o Dictionaries. With the Product-TM Systems approach we prove that at each selection of a pair of parameters the maximal energy may be attained, and, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2088","kind":"arxiv","version":4},"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"}