{"id":"https://openalex.org/W7125192499","doi":"https://doi.org/10.48550/arxiv.2601.12572","title":"A Functorial Approach to Multi-Space Interpolation with Function Parameters","display_name":"A Functorial Approach to Multi-Space Interpolation with Function Parameters","publication_year":2026,"publication_date":"2026-01-18","ids":{"openalex":"https://openalex.org/W7125192499","doi":"https://doi.org/10.48550/arxiv.2601.12572"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2601.12572","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.12572","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.2601.12572","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030079382","display_name":"Thomas Lamby","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lamby, Thomas","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5123530421","display_name":"Samuel Nicolay","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nicolay, Samuel","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030079382"],"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":0.29989999532699585,"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":0.29989999532699585,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.21160000562667847,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.10520000010728836,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6485999822616577},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5429999828338623},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5127999782562256},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.49799999594688416},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.46860000491142273},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4408000111579895},{"id":"https://openalex.org/keywords/nearest-neighbor-interpolation","display_name":"Nearest-neighbor interpolation","score":0.438400000333786},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4198000133037567}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7817999720573425},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6485999822616577},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5429999828338623},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5127999782562256},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.49799999594688416},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.46860000491142273},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4580000042915344},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4408000111579895},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.438400000333786},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4198000133037567},{"id":"https://openalex.org/C6183050","wikidata":"https://www.wikidata.org/wiki/Q3058180","display_name":"Interpolation space","level":4,"score":0.4171000123023987},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37310001254081726},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.364300012588501},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.35339999198913574},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.3384000062942505},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.33000001311302185},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.320499986410141},{"id":"https://openalex.org/C143542097","wikidata":"https://www.wikidata.org/wiki/Q3153554","display_name":"Inverse quadratic interpolation","level":5,"score":0.313400000333786},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.29249998927116394},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2865999937057495},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2732999920845032},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.271699994802475},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.27160000801086426},{"id":"https://openalex.org/C203332170","wikidata":"https://www.wikidata.org/wiki/Q6334079","display_name":"Multivariate interpolation","level":3,"score":0.2702000141143799},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.2653999924659729},{"id":"https://openalex.org/C69151251","wikidata":"https://www.wikidata.org/wiki/Q846537","display_name":"Generalized function","level":2,"score":0.2648000121116638}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2601.12572","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.12572","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.2601.12572","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.12572","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],"introduce":[1],"an":[2],"extension":[3],"of":[4,31,56],"interpolation":[5,55],"theory":[6],"to":[7],"more":[8],"than":[9],"two":[10],"spaces":[11,34,60],"by":[12],"employing":[13],"a":[14,19,48,62],"functional":[15],"parameter,":[16],"while":[17],"retaining":[18],"fully":[20],"functorial":[21],"and":[22,35,44,80],"systematic":[23],"framework.":[24],"This":[25],"approach":[26],"allows":[27],"for":[28,71],"the":[29,54],"construction":[30],"generalized":[32,58,63],"intermediate":[33],"ensures":[36],"stability":[37],"under":[38],"natural":[39],"operations":[40],"such":[41],"as":[42],"powers":[43],"convex":[45],"combinations.":[46],"As":[47],"significant":[49],"application,":[50],"we":[51],"demonstrate":[52],"that":[53],"multiple":[57],"Sobolev":[59],"yields":[61],"Besov":[64],"space.":[65],"Our":[66],"framework":[67],"provides":[68],"explicit":[69],"tools":[70],"handling":[72],"multi-parameter":[73],"interpolation,":[74],"highlighting":[75],"both":[76],"its":[77],"theoretical":[78],"robustness":[79],"practical":[81],"relevance.":[82]},"counts_by_year":[],"updated_date":"2026-01-22T23:33:04.759266","created_date":"2026-01-22T00:00:00"}