{"id":"https://openalex.org/W7160616794","doi":"https://doi.org/10.48550/arxiv.2605.05610","title":"Vector field multiplier operators and matrix-valued kernel quasi-interpolation","display_name":"Vector field multiplier operators and matrix-valued kernel quasi-interpolation","publication_year":2026,"publication_date":"2026-05-07","ids":{"openalex":"https://openalex.org/W7160616794","doi":"https://doi.org/10.48550/arxiv.2605.05610"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.05610","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05610","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":null,"license_id":null,"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.2605.05610","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135677603","display_name":"Zhengjie Sun","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sun, Zhengjie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100432851","display_name":"Biao Huang","orcid":"https://orcid.org/0000-0001-9082-2216"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Biao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135664239","display_name":"Xingping Sun","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sun, Xingping","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"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/T10514","display_name":"Numerical methods in engineering","score":0.24449999630451202,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.24449999630451202,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.14190000295639038,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.1281999945640564,"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/robustness","display_name":"Robustness (evolution)","score":0.5331000089645386},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5325999855995178},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.4805999994277954},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.4474000036716461},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.41769999265670776},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.4165000021457672},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.4131999909877777},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.413100004196167},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.3587000072002411}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7856000065803528},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5331000089645386},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5325999855995178},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.4805999994277954},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47929999232292175},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.4474000036716461},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.41769999265670776},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.4165000021457672},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.4131999909877777},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.413100004196167},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3587000072002411},{"id":"https://openalex.org/C2456702","wikidata":"https://www.wikidata.org/wiki/Q1375954","display_name":"Vector-valued function","level":2,"score":0.3571999967098236},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.352400004863739},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.3456999957561493},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.3330000042915344},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.33009999990463257},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3287999927997589},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.3127000033855438},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29789999127388},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.29109999537467957},{"id":"https://openalex.org/C79587385","wikidata":"https://www.wikidata.org/wiki/Q2638931","display_name":"Convolution theorem","level":5,"score":0.28790000081062317},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.2703999876976013},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.26510000228881836},{"id":"https://openalex.org/C152303783","wikidata":"https://www.wikidata.org/wiki/Q855949","display_name":"Sinc function","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.25270000100135803},{"id":"https://openalex.org/C129683796","wikidata":"https://www.wikidata.org/wiki/Q430450","display_name":"Microlocal analysis","level":4,"score":0.250900000333786},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.05610","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05610","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.05610","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05610","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"develop":[1],"and":[2,33,133],"analyze":[3],"a":[4,88],"class":[5],"of":[6,25,62,81,90,127,136],"matrix-valued":[7],"spherical-convolution":[8],"kernels":[9,27],"stemming":[10],"from":[11],"scaled":[12],"zonal":[13,42],"functions":[14],"on":[15,39,72,77],"$\\mathbb{S}^2,$":[16],"the":[17,29,40,63,73,82,99,121,137,145],"unit":[18],"sphere":[19],"embedded":[20],"in":[21,98,141],"$\\mathbb{R}^3$.":[22],"The":[23,44,103,111,130],"construct":[24],"these":[26],"utilizes":[28],"Legendre":[30],"differential":[31],"equation":[32],"requires":[34],"less":[35],"stringent":[36],"regularity":[37],"conditions":[38],"original":[41],"kernels.":[43],"induced":[45],"integral":[46],"operators":[47],"are":[48],"simple":[49],"Fourier-Legendre":[50],"multipliers":[51],"that":[52,93],"not":[53],"only":[54],"deliver":[55],"optimal":[56],"Sobolev":[57],"error":[58],"estimates":[59],"(in":[60],"terms":[61],"scaling":[64],"parameter)":[65],"but":[66],"also":[67],"yield":[68],"natural":[69],"Helmholtz-Hodge":[70],"decompositions":[71],"$L_2$-tangential":[74],"vector":[75,101,148],"fields":[76],"$\\mathbb{S}^2$.":[78],"Via":[79],"discretization":[80],"underlying":[83],"convolution":[84,122],"integrals,":[85],"we":[86],"harvest":[87],"family":[89],"vector-valued":[91],"quasi-interpolants":[92],"accomplish":[94],"our":[95],"approximation":[96],"goal":[97],"divergence/curl-free":[100],"field.":[102],"quasi-interpolation":[104,138],"algorithm":[105,139],"is":[106,114],"robust":[107],"against":[108],"noisy":[109],"data.":[110],"implementation":[112],"process":[113],"adaptive":[115],"to":[116,144],"human-improvision,":[117],"involving":[118],"neither":[119],"evaluating":[120],"integrals":[123],"nor":[124],"solving":[125],"systems":[126],"linear":[128],"equations.":[129],"computational":[131],"efficiency":[132],"executory":[134],"robustness":[135],"stand":[140],"sharp":[142],"contrast":[143],"existing":[146],"kernel-based":[147],"field":[149],"interpolation":[150],"method.":[151]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-09T00:00:00"}