{"id":"https://openalex.org/W7204876107","doi":"https://doi.org/10.48550/arxiv.2608.29442","title":"An Ellipse Criterion for Exact Nonuniqueness in the Planar Interior Radon Problem","display_name":"An Ellipse Criterion for Exact Nonuniqueness in the Planar Interior Radon Problem","publication_year":2026,"publication_date":"2026-08-29","ids":{"openalex":"https://openalex.org/W7204876107","doi":"https://doi.org/10.48550/arxiv.2608.29442"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29442","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29442","pdf_url":"https://arxiv.org/pdf/2608.29442","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.29442","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044197620","display_name":"Christian H\u00e4gg","orcid":"https://orcid.org/0000-0002-8501-3622","observed_orcids":["https://orcid.org/0000-0002-8501-3622"]},"institutions":[{"id":"https://openalex.org/I161593684","display_name":"Stockholm University","ror":"https://ror.org/05f0yaq80","country_code":"SE","type":"education","lineage":["https://openalex.org/I161593684"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"H\u00e4gg, Christian","raw_affiliation_strings":["Department of Mathematics , Stockholm University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Stockholm University","institution_ids":["https://openalex.org/I161593684"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044197620"],"corresponding_institution_ids":["https://openalex.org/I161593684"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9663000106811523,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9663000106811523,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.024399999529123306,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/open-convex-sets","display_name":"open convex sets","score":0.7730000019073486},{"id":"https://openalex.org/keywords/compactly-supported-functions","display_name":"compactly supported functions","score":0.656000018119812},{"id":"https://openalex.org/keywords/l1-functions","display_name":"L1 functions","score":0.7480000257492065},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.4959999918937683},{"id":"https://openalex.org/keywords/integral-geometry","display_name":"integral geometry","score":0.44699999690055847}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7771000266075134},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7361999750137329},{"id":"https://openalex.org/C74261601","wikidata":"https://www.wikidata.org/wiki/Q40112","display_name":"Ellipse","level":2,"score":0.7289000153541565},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6121000051498413},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5981000065803528},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.5609999895095825},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5146999955177307},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.43320000171661377},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4237000048160553},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.3986999988555908},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.3792000114917755},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.37689998745918274},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3628999888896942},{"id":"https://openalex.org/C90296322","wikidata":"https://www.wikidata.org/wiki/Q619776","display_name":"Concentric","level":2,"score":0.36039999127388},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33489999175071716},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.33149999380111694},{"id":"https://openalex.org/C545943180","wikidata":"https://www.wikidata.org/wiki/Q1133","display_name":"Radon","level":2,"score":0.32679998874664307},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.31839999556541443},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.3118000030517578},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.31139999628067017},{"id":"https://openalex.org/C92928283","wikidata":"https://www.wikidata.org/wiki/Q4949981","display_name":"Bounded deformation","level":4,"score":0.3100000023841858},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.2896000146865845},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.2766000032424927},{"id":"https://openalex.org/C2777105136","wikidata":"https://www.wikidata.org/wiki/Q827230","display_name":"Lebesgue measure","level":3,"score":0.266400009393692},{"id":"https://openalex.org/C174676996","wikidata":"https://www.wikidata.org/wiki/Q2126650","display_name":"Radon measure","level":3,"score":0.2605000138282776},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.2540999948978424}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29442","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29442","pdf_url":"https://arxiv.org/pdf/2608.29442","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.29442","doi":"https://doi.org/10.48550/arxiv.2608.29442","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29442","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.29442","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29442","pdf_url":"https://arxiv.org/pdf/2608.29442","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204876107.pdf","grobid_xml":"https://content.openalex.org/works/W7204876107.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W2038753442","https://openalex.org/W2157597287","https://openalex.org/W3009604651","https://openalex.org/W3131596041","https://openalex.org/W4211179796","https://openalex.org/W4296844654","https://openalex.org/W4413080524"],"related_works":["https://openalex.org/W4413080524","https://openalex.org/W1944612685","https://openalex.org/W2476056737","https://openalex.org/W2094649784","https://openalex.org/W2020239290","https://openalex.org/W2026875953","https://openalex.org/W1986985193","https://openalex.org/W3009604651","https://openalex.org/W3131596041","https://openalex.org/W2062683658"],"abstract_inverted_index":{"We":[0],"characterize":[1],"exact":[2],"nonuniqueness":[3],"in":[4,25,56,75],"the":[5,26,35,46,49,57,76,93,96,101],"planar":[6],"interior":[7],"Radon":[8,81],"problem":[9],"for":[10,64,100],"arbitrary":[11],"pairs":[12],"of":[13,48,111,118],"open":[14,91],"convex":[15],"sets.":[16],"There":[17],"exists":[18],"a":[19,65],"nonzero":[20,66],"smooth":[21],"function":[22,68],"compactly":[23,54,73],"supported":[24],"first":[27,58,77],"set":[28,37,51,78],"whose":[29,69,80],"integral":[30],"over":[31],"every":[32],"line":[33],"meeting":[34],"second":[36,50],"vanishes":[38,83],"if":[39,42],"and":[40,52,79,114],"only":[41],"an":[43],"ellipse":[44],"contains":[45],"closure":[47],"is":[53,72],"contained":[55,74],"set.":[59],"The":[60],"same":[61],"criterion":[62,94],"holds":[63],"$L^1$":[67],"essential":[70],"support":[71],"transform":[82],"almost":[84],"everywhere":[85],"on":[86],"those":[87],"lines.":[88],"For":[89],"concentric":[90],"squares,":[92],"gives":[95],"sharp":[97],"threshold":[98],"$1/\\sqrt2$":[99],"inner-to-outer":[102],"half-side":[103],"ratio.":[104],"This":[105],"yields":[106],"counterexamples":[107],"to":[108,115],"Conjecture":[109],"1.2":[110],"Boman":[112,119],"(2021)":[113],"Theorem":[116],"40.1":[117],"(2025).":[120]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
