{"paper":{"title":"On a family of differential-reflection operators: intertwining operators and Fourier transform of rapidly decreasing functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Asma Boussen, Mohamed Sifi, Salem Ben Said","submitted_at":"2015-07-03T15:07:47Z","abstract_excerpt":"We introduce a family of differential-reflection operators $\\Lambda_{A, \\varepsilon}$ acting on smooth functions defined on $\\mathbb R.$ Here $A$ is a Strum-Liouville function with additional hypotheses and $\\varepsilon\\in \\mathbb R.$ For special pairs $(A,\\varepsilon),$ we recover Dunkl's, Heckman's and Cherednik's operators (in one dimension). The spectral problem for the operators $\\Lambda_{A, \\varepsilon}$ is studied. In particular, we obtain suitable growth estimates for the eigenfunctions of $\\Lambda_{A, \\varepsilon}$.\n  As the operators $\\Lambda_{A, \\varepsilon}$ are mixture of $d/dx$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00936","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"}