{"id":"https://openalex.org/W7140831827","doi":"https://doi.org/10.48550/arxiv.2603.23732","title":"Orthogonal polynomials for the de Rham complex on the disk and cylinder","display_name":"Orthogonal polynomials for the de Rham complex on the disk and cylinder","publication_year":2026,"publication_date":"2026-03-24","ids":{"openalex":"https://openalex.org/W7140831827","doi":"https://doi.org/10.48550/arxiv.2603.23732"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.23732","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23732","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.23732","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010027385","display_name":"Sheehan Olver","orcid":"https://orcid.org/0000-0001-6920-0826"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Olver, Sheehan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010027385"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.07450000196695328,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.07450000196695328,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.07129999995231628,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.0658000037074089,"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/zernike-polynomials","display_name":"Zernike polynomials","score":0.8647000193595886},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.7627000212669373},{"id":"https://openalex.org/keywords/curl","display_name":"Curl (programming language)","score":0.5806000232696533},{"id":"https://openalex.org/keywords/cylinder","display_name":"Cylinder","score":0.45260000228881836},{"id":"https://openalex.org/keywords/orthogonal-transformation","display_name":"Orthogonal transformation","score":0.4345000088214874},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.4260999858379364},{"id":"https://openalex.org/keywords/discrete-orthogonal-polynomials","display_name":"Discrete orthogonal polynomials","score":0.4124000072479248},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4068000018596649},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.39629998803138733}],"concepts":[{"id":"https://openalex.org/C92423082","wikidata":"https://www.wikidata.org/wiki/Q132146","display_name":"Zernike polynomials","level":3,"score":0.8647000193595886},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.7627000212669373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7239000201225281},{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.5806000232696533},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4932999908924103},{"id":"https://openalex.org/C203311528","wikidata":"https://www.wikidata.org/wiki/Q34132","display_name":"Cylinder","level":2,"score":0.45260000228881836},{"id":"https://openalex.org/C54940322","wikidata":"https://www.wikidata.org/wiki/Q3997740","display_name":"Orthogonal transformation","level":2,"score":0.4345000088214874},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.4260999858379364},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.4124000072479248},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4068000018596649},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.39629998803138733},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3955000042915344},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.39329999685287476},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.3864000141620636},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.374099999666214},{"id":"https://openalex.org/C187064257","wikidata":"https://www.wikidata.org/wiki/Q3306808","display_name":"Orthogonal basis","level":2,"score":0.3732999861240387},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.36070001125335693},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.35530000925064087},{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.32330000400543213},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C118431652","wikidata":"https://www.wikidata.org/wiki/Q17098827","display_name":"Mehler\u2013Heine formula","level":5,"score":0.2865000069141388},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28619998693466187},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2718000113964081},{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.263700008392334},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.2531999945640564},{"id":"https://openalex.org/C135925592","wikidata":"https://www.wikidata.org/wiki/Q2637908","display_name":"Orthogonal functions","level":2,"score":0.2529999911785126}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.23732","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23732","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.23732","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23732","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,128],"paper":[1],"constructs":[2],"polynomial":[3],"bases":[4,133,146],"that":[5,28,48,71],"capture":[6],"the":[7,10,45,52,79,82,95,114,126,148],"structure":[8],"of":[9,38,81,97,113],"de":[11,149],"Rham":[12,150],"complex":[13,151],"with":[14,65,121,136],"boundary":[15,80],"conditions":[16],"in":[17,25,134],"disks":[18],"and":[19,23,40,102,143],"cylinders":[20,135],"(both":[21],"periodic":[22],"finite)":[24],"a":[26,68,91,110],"way":[27],"respects":[29],"rotational":[30],"symmetry.":[31],"The":[32,84],"starting":[33],"point":[34],"is":[35,109],"explicit":[36],"constructions":[37],"vector":[39,73,87],"matrix":[41,69],"orthogonal":[42,63,88,120],"polynomials":[43,64,74,89,117],"on":[44,78,125],"unit":[46],"disk":[47],"are":[49,119],"analogous":[50],"to":[51,60,67,75,94,123,132],"(scalar)":[53],"generalised":[54,99],"Zernike":[55,100,116],"polynomials.":[56],"We":[57],"use":[58],"these":[59],"build":[61],"new":[62],"respect":[66,122],"weight":[70],"forces":[72],"be":[76],"normal":[77],"disk.":[83,127],"resulting":[85],"weighted":[86,98],"have":[90],"simple":[92,137],"connection":[93],"gradient":[96],"polynomials,":[101],"their":[103,140],"curl":[104,142],"(i.e.":[105],"vorticity":[106],"or":[107],"rot)":[108],"constant":[111],"multiple":[112],"standard":[115],"which":[118],"$L^2$":[124],"construction":[129],"naturally":[130],"leads":[131],"recurrences":[138],"relating":[139],"gradient,":[141],"divergence.":[144],"These":[145],"decouple":[147],"into":[152],"small":[153],"exact":[154],"sub-complexes.":[155]},"counts_by_year":[],"updated_date":"2026-03-27T06:05:27.210665","created_date":"2026-03-27T00:00:00"}
