{"id":"https://openalex.org/W7117980022","doi":"https://doi.org/10.48550/arxiv.2512.24964","title":"Approximating evolution operators of linear delay equations: a general framework for the convergence analysis","display_name":"Approximating evolution operators of linear delay equations: a general framework for the convergence analysis","publication_year":2025,"publication_date":"2025-12-31","ids":{"openalex":"https://openalex.org/W7117980022","doi":"https://doi.org/10.48550/arxiv.2512.24964"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2512.24964","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.24964","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.2512.24964","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036438633","display_name":"Alessia And\u00f2","orcid":"https://orcid.org/0000-0002-4051-2049"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"and\u00f2, Alessia","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121793603","display_name":"Giusy Bosco","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bosco, Giusy","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080897837","display_name":"Dimitri Breda","orcid":"https://orcid.org/0000-0002-4641-1126"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Breda, Dimitri","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059733803","display_name":"Davide Liessi","orcid":"https://orcid.org/0000-0002-2649-1253"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liessi, Davide","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5036438633"],"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.2833000123500824,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.2833000123500824,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.21480000019073486,"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/T11416","display_name":"Numerical methods for differential equations","score":0.1289999932050705,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/generality","display_name":"Generality","score":0.715499997138977},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7020000219345093},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.546500027179718},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5081999897956848},{"id":"https://openalex.org/keywords/linear-operators","display_name":"Linear operators","score":0.4862000048160553},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.47679999470710754},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.4683000147342682},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.364300012588501}],"concepts":[{"id":"https://openalex.org/C2780767217","wikidata":"https://www.wikidata.org/wiki/Q5532421","display_name":"Generality","level":2,"score":0.715499997138977},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7020000219345093},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6870999932289124},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6297000050544739},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.546500027179718},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5081999897956848},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.4862000048160553},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.47679999470710754},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4683000147342682},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3776000142097473},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.364300012588501},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.33079999685287476},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.3077999949455261},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3061999976634979},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3034999966621399},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.2806999981403351},{"id":"https://openalex.org/C14928880","wikidata":"https://www.wikidata.org/wiki/Q1512559","display_name":"Normal convergence","level":4,"score":0.27549999952316284},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26919999718666077},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.26429998874664307},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2531999945640564}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2512.24964","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.24964","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.2512.24964","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.24964","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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4620111882686615}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,36],"consider":[1],"the":[2,13,24,31,47,62,66,69,72,82,101,104,118],"problem":[3],"of":[4,8,15,27,33,46,51,58,65,71,103,113],"discretizing":[5],"evolution":[6],"operators":[7,48],"linear":[9],"delay":[10],"equations":[11,29],"with":[12],"aim":[14],"approximating":[16],"their":[17],"spectra,":[18],"which":[19,91,120],"is":[20],"useful":[21],"in":[22,95,117],"investigating":[23],"stability":[25],"properties":[26,64],"(nonlinear)":[28],"via":[30],"principle":[32],"linearized":[34],"stability.":[35],"develop":[37],"a":[38,44,52,56,111,124],"general":[39],"convergence":[40,70,126],"analysis":[41],"based":[42,87],"on":[43,76,88],"reformulation":[45],"by":[49],"means":[50],"fixed-point":[53],"equation,":[54],"providing":[55],"list":[57],"hypotheses":[59],"related":[60],"to":[61,110],"regularization":[63],"equation":[67],"and":[68],"chosen":[73],"approximation":[74],"techniques":[75],"suitable":[77],"subspaces.":[78],"This":[79],"framework":[80],"unifies":[81],"proofs":[83],"for":[84],"some":[85],"methods":[86],"pseudospectral":[89],"discretization,":[90],"we":[92,106],"present":[93],"here":[94],"this":[96],"new":[97],"form.":[98],"To":[99],"exemplify":[100],"generality":[102],"framework,":[105],"also":[107],"apply":[108],"it":[109],"method":[112],"weighted":[114],"residuals":[115],"found":[116],"literature,":[119],"was":[121],"previously":[122],"lacking":[123],"formal":[125],"analysis.":[127]},"counts_by_year":[],"updated_date":"2026-01-02T23:15:32.796280","created_date":"2026-01-02T00:00:00"}