{"id":"https://openalex.org/W7213928435","doi":"https://doi.org/10.48550/arxiv.2609.21098","title":"Delay equations with measure-valued coefficients: From Carath\u00e9odory solutions to measurable semiflows","display_name":"Delay equations with measure-valued coefficients: From Carath\u00e9odory solutions to measurable semiflows","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213928435","doi":"https://doi.org/10.48550/arxiv.2609.21098"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.21098","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21098","pdf_url":"https://arxiv.org/pdf/2609.21098","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/2609.21098","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018748329","display_name":"Marek Kryspin","orcid":"https://orcid.org/0000-0001-5525-273X","observed_orcids":["https://orcid.org/0000-0001-5525-273X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kryspin, Marek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5018748329"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.6304000020027161,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.6304000020027161,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.34200000762939453,"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"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.01119999960064888,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/delay-differential-equations","display_name":"delay differential equations","score":0.9509999752044678},{"id":"https://openalex.org/keywords/signed-measures","display_name":"signed measures","score":0.7609999775886536},{"id":"https://openalex.org/keywords/caratheodory-solutions","display_name":"Carath\u00e9odory solutions","score":0.9610000252723694},{"id":"https://openalex.org/keywords/well-posedness","display_name":"well-posedness","score":0.7799999713897705},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"weak convergence","score":0.7860000133514404},{"id":"https://openalex.org/keywords/total-variation-bounds","display_name":"total variation bounds","score":0.7450000047683716},{"id":"https://openalex.org/keywords/skew-product-semiflows","display_name":"skew-product semiflows","score":0.7680000066757202},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"ergodic theory","score":0.828000009059906},{"id":"https://openalex.org/keywords/lyapunov-exponents","display_name":"Lyapunov exponents","score":0.9559999704360962},{"id":"https://openalex.org/keywords/distributed-delay","display_name":"distributed delay","score":0.8399999737739563}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8877000212669373},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.6567000150680542},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5152999758720398},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4733999967575073},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.4537999927997589},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.45179998874664307},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.435699999332428},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.42570000886917114},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42500001192092896},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4207000136375427},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.41179999709129333},{"id":"https://openalex.org/C118733216","wikidata":"https://www.wikidata.org/wiki/Q332504","display_name":"Absolute continuity","level":2,"score":0.4059999883174896},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.35280001163482666},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.34439998865127563},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.3425999879837036},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.31060001254081726},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3009999990463257},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.29820001125335693},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C88757350","wikidata":"https://www.wikidata.org/wiki/Q1557613","display_name":"L\u00e9vy process","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C553313952","wikidata":"https://www.wikidata.org/wiki/Q1537963","display_name":"H\u00f6lder condition","level":2,"score":0.2660999894142151},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.21098","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21098","pdf_url":"https://arxiv.org/pdf/2609.21098","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.2609.21098","doi":"https://doi.org/10.48550/arxiv.2609.21098","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.21098","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.21098","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21098","pdf_url":"https://arxiv.org/pdf/2609.21098","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/W7213928435.pdf","grobid_xml":"https://content.openalex.org/works/W7213928435.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4407868477","https://openalex.org/W7127381462"],"related_works":["https://openalex.org/W2226672368","https://openalex.org/W3215974001","https://openalex.org/W2908959051","https://openalex.org/W1190322485","https://openalex.org/W4415981043","https://openalex.org/W2555870256","https://openalex.org/W4404422923","https://openalex.org/W2023038593","https://openalex.org/W4281624252","https://openalex.org/W3177120223"],"abstract_inverted_index":{"We":[0,34],"study":[1],"linear":[2,139],"delay":[3,7,23],"differential":[4],"equations":[5],"whose":[6],"terms":[8],"are":[9],"represented":[10],"by":[11,129],"time-dependent":[12],"finite":[13,158],"signed":[14,68],"measures.":[15],"This":[16,84],"framework":[17],"accommodates":[18],"discrete,":[19],"distributed,":[20],"and":[21,41,54,78,144,153,164,174],"singular":[22],"contributions":[24],"without":[25],"requiring":[26],"continuity":[27,120],"of":[28,44,63,90,100,111,119,156],"the":[29,38,47,64,71,94,101,112,116,122,154,170],"coefficient":[30,76],"paths":[31],"in":[32,37,121],"time.":[33],"establish":[35],"well-posedness":[36],"Carath\u00e9odory":[39],"sense":[40],"sequential":[42],"dependence":[43],"solutions":[45],"on":[46,70,93,142,176],"measure-valued":[48],"parameters":[49],"under":[50],"almost-everywhere":[51],"weak-*":[52,124],"convergence":[53],"a":[55,67,91,130,157],"common":[56],"total":[57],"variation":[58],"bound.":[59],"A":[60,104],"central":[61],"part":[62],"analysis":[65],"associates":[66],"measure":[69],"time--delay":[72],"domain":[73],"with":[74,169],"each":[75],"path":[77],"establishes":[79],"an":[80],"equivalent":[81,88],"integral":[82],"formulation.":[83],"representation":[85],"yields":[86],"three":[87],"characterizations":[89],"$\u03c3$-algebra":[92],"parameter":[95],"space":[96],"suited":[97],"to":[98,137],"measurability":[99,110],"continuation":[102],"operator.":[103],"measurable":[105,138],"fixed-point":[106],"argument":[107],"then":[108],"provides":[109],"solution":[113],"maps,":[114],"despite":[115],"possible":[117],"failure":[118],"product":[123],"topology.":[125],"For":[126],"coefficients":[127],"generated":[128],"measure-preserving":[131],"base":[132],"flow,":[133],"these":[134],"results":[135],"lead":[136],"skew-product":[140],"semiflows":[141],"continuous":[143,146],"absolutely":[145],"phase":[147],"spaces.":[148,178],"Under":[149],"additional":[150],"ergodic":[151],"hypotheses":[152],"assumption":[155],"top":[159],"Lyapunov":[160,172],"exponent,":[161],"eventual":[162],"compactness":[163],"regularization":[165],"yield":[166],"Oseledets":[167],"decompositions":[168],"same":[171],"exponents":[173],"multiplicities":[175],"both":[177]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-22T00:00:00"}