{"id":"https://openalex.org/W7214054375","doi":"https://doi.org/10.48550/arxiv.2609.23740","title":"Explicit diagonalization of the linearized Calder\u00f3n problem on the disk: multiplicity normalization and exponential spectral attenuation","display_name":"Explicit diagonalization of the linearized Calder\u00f3n problem on the disk: multiplicity normalization and exponential spectral attenuation","publication_year":2026,"publication_date":"2026-09-20","ids":{"openalex":"https://openalex.org/W7214054375","doi":"https://doi.org/10.48550/arxiv.2609.23740"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.23740","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23740","pdf_url":"https://arxiv.org/pdf/2609.23740","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/2609.23740","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058599589","display_name":"William R. B. Lionheart","orcid":"https://orcid.org/0000-0003-0971-4678","observed_orcids":["https://orcid.org/0000-0003-0971-4678"]},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Lionheart, William Robert Breckon","raw_affiliation_strings":["Department of Mathematics , The University of Manchester , Manchester M13 9PL , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , The University of Manchester , Manchester M13 9PL , United Kingdom","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058599589"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.9824000000953674,"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":0.9824000000953674,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.014299999922513962,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/calderon-problem","display_name":"Calder\u00f3n problem","score":0.9240000247955322},{"id":"https://openalex.org/keywords/linearized-inversion","display_name":"linear inversion","score":0.6819999814033508},{"id":"https://openalex.org/keywords/schrodinger-operators","display_name":"Schr\u00f6dinger operators","score":0.7129999995231628},{"id":"https://openalex.org/keywords/unit-disk","display_name":"unit disk","score":0.8730000257492065},{"id":"https://openalex.org/keywords/angular-dependence","display_name":"angular dependence","score":0.7229999899864197},{"id":"https://openalex.org/keywords/normal-operators","display_name":"normal operators","score":0.5370000004768372}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6420999765396118},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.5636000037193298},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5080999732017517},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.45969998836517334},{"id":"https://openalex.org/C184652730","wikidata":"https://www.wikidata.org/wiki/Q2357982","display_name":"Attenuation","level":2,"score":0.4162999987602234},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.39559999108314514},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.37700000405311584},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33660000562667847},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3353999853134155},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.3278999924659729},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.273499995470047},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.25920000672340393},{"id":"https://openalex.org/C35958075","wikidata":"https://www.wikidata.org/wiki/Q1425077","display_name":"Spectral theorem","level":3,"score":0.2556999921798706},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.25200000405311584}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.23740","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23740","pdf_url":"https://arxiv.org/pdf/2609.23740","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.2609.23740","doi":"https://doi.org/10.48550/arxiv.2609.23740","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.23740","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:2609.23740","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23740","pdf_url":"https://arxiv.org/pdf/2609.23740","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214054375.pdf","grobid_xml":"https://content.openalex.org/works/W7214054375.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2586085846","https://openalex.org/W4297824138","https://openalex.org/W4391766603","https://openalex.org/W3205011085","https://openalex.org/W1986353154","https://openalex.org/W3008824220","https://openalex.org/W2127254230","https://openalex.org/W1988150402","https://openalex.org/W4405783307","https://openalex.org/W2080218377"],"abstract_inverted_index":{"We":[0,19],"study":[1],"the":[2,7,12,16,37,46,51,60],"full":[3,52],"angular":[4],"dependence":[5],"of":[6,11,26],"linearized":[8,38,56],"Schr\u00f6dinger":[9],"form":[10],"Calder\u00f3n":[13],"problem":[14],"on":[15,59],"unit":[17],"disk.":[18,61],"obtain":[20],"an":[21],"explicit":[22],"continuous":[23],"spectral":[24],"diagonalization":[25,49],"its":[27],"normal":[28],"operator":[29],"and":[30],"hence":[31],"a":[32],"generalized":[33],"singular":[34],"system":[35],"for":[36,50],"forward":[39],"map.":[40],"To":[41],"our":[42],"knowledge,":[43],"this":[44],"is":[45],"first":[47],"such":[48],"angularly":[53],"dependent,":[54],"multiplicity-normalized":[55],"measurement":[57],"map":[58]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}
