{"paper":{"title":"Perturbed lattice crosses and Heisenberg uniqueness pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Danylo Radchenko, Jo\\~ao P. G. Ramos","submitted_at":"2024-10-06T17:25:52Z","abstract_excerpt":"This work focuses on two questions raised by H. Hedenmalm and A. Montes-Rodr\\'iguez on Heisenberg Uniqueness Pairs for perturbed lattice crosses.\n  The first of them deals with a complete characterization of $\\beta>0$ for which, for a fixed $\\theta \\in \\mathbb{R},$ the translated lattice cross $\\Lambda_{\\beta}^{\\theta} = ((\\mathbb{Z} + \\{\\theta\\}) \\times \\{0\\}) \\cup (\\{0\\} \\times \\beta \\mathbb{Z})$ satisfies that $(\\Gamma,\\Lambda_{\\beta}^{\\theta})$ is a Heisenberg Uniqueness Pair, where $\\Gamma$ is the hyperbola in $\\mathbb{R}^2$ with axes as asymptotes. We show that $(\\Gamma,\\Lambda_{\\beta}^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.04557","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/2410.04557/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"}