{"id":"https://openalex.org/W2981095586","doi":"https://doi.org/10.1007/s00332-019-09598-5","title":"Spectrum of the Koopman Operator, Spectral Expansions in Functional Spaces, and State-Space Geometry","display_name":"Spectrum of the Koopman Operator, Spectral Expansions in Functional Spaces, and State-Space Geometry","publication_year":2019,"publication_date":"2019-12-06","ids":{"openalex":"https://openalex.org/W2981095586","doi":"https://doi.org/10.1007/s00332-019-09598-5","mag":"2981095586"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-019-09598-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-019-09598-5","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1702.07597","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014334832","display_name":"Igor Mezi\u0107","orcid":"https://orcid.org/0000-0002-2873-9013"},"institutions":[{"id":"https://openalex.org/I154347574","display_name":"University of Rijeka","ror":"https://ror.org/05r8dqr10","country_code":"HR","type":"education","lineage":["https://openalex.org/I154347574"]},{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["HR","US"],"is_corresponding":true,"raw_author_name":"Igor Mezi\u0107","raw_affiliation_strings":["Mechanical Engineering and Mathematics, University of California Santa Barbara, Santa Barbara, CA, 93106, USA","University of Rijeka, Rijeka, Croatia","Mechanical Engineering and Mathematics, University of California Santa Barbara, Santa Barbara, USA"],"affiliations":[{"raw_affiliation_string":"Mechanical Engineering and Mathematics, University of California Santa Barbara, Santa Barbara, CA, 93106, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"University of Rijeka, Rijeka, Croatia","institution_ids":["https://openalex.org/I154347574"]},{"raw_affiliation_string":"Mechanical Engineering and Mathematics, University of California Santa Barbara, Santa Barbara, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014334832"],"corresponding_institution_ids":["https://openalex.org/I154347574","https://openalex.org/I154570441"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.2957,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.80714428,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"30","issue":"5","first_page":"2091","last_page":"2145"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9850999712944031,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.833823561668396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6897205114364624},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.5917214155197144},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.5402562022209167},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.523697018623352},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5189806818962097},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49685171246528625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47018352150917053},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4645307660102844},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.45381420850753784},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.4267062544822693},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34662383794784546},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.2277543544769287},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13088497519493103},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08497902750968933}],"concepts":[{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.833823561668396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6897205114364624},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.5917214155197144},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.5402562022209167},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.523697018623352},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5189806818962097},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49685171246528625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47018352150917053},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4645307660102844},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.45381420850753784},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.4267062544822693},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34662383794784546},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2277543544769287},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13088497519493103},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08497902750968933},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00332-019-09598-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-019-09598-5","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1702.07597","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1702.07597","pdf_url":"https://arxiv.org/pdf/1702.07597","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2981095586","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1702.07597v2","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1702.07597","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1702.07597","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":"pmh:oai:arXiv.org:1702.07597","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1702.07597","pdf_url":"https://arxiv.org/pdf/1702.07597","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5172387102","display_name":null,"funder_award_id":"W911NF-11-1-0511","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G6520853767","display_name":null,"funder_award_id":"W911NF-14-1-0359","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G6961067593","display_name":null,"funder_award_id":"HR0011-16-C-0116","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"}],"funders":[{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W86907751","https://openalex.org/W1497901417","https://openalex.org/W1551756560","https://openalex.org/W1730162945","https://openalex.org/W1975487887","https://openalex.org/W1977106683","https://openalex.org/W1983964647","https://openalex.org/W1990636640","https://openalex.org/W1994953169","https://openalex.org/W1995043136","https://openalex.org/W1997054581","https://openalex.org/W2013734438","https://openalex.org/W2014356541","https://openalex.org/W2016315007","https://openalex.org/W2022911541","https://openalex.org/W2067035505","https://openalex.org/W2069159682","https://openalex.org/W2069974243","https://openalex.org/W2073505808","https://openalex.org/W2079647387","https://openalex.org/W2083115202","https://openalex.org/W2089876099","https://openalex.org/W2094686470","https://openalex.org/W2101222417","https://openalex.org/W2114876173","https://openalex.org/W2128949314","https://openalex.org/W2164954534","https://openalex.org/W2172945660","https://openalex.org/W2289369672","https://openalex.org/W2289725842","https://openalex.org/W2319450871","https://openalex.org/W2482944896","https://openalex.org/W2505615364","https://openalex.org/W2551318894","https://openalex.org/W2551533301","https://openalex.org/W2567118861","https://openalex.org/W2775659970","https://openalex.org/W2901625726","https://openalex.org/W2906206094","https://openalex.org/W3038118776","https://openalex.org/W3105713006","https://openalex.org/W3133989388","https://openalex.org/W3141151088","https://openalex.org/W4239513491","https://openalex.org/W4244334050","https://openalex.org/W4294967943","https://openalex.org/W4302585512","https://openalex.org/W6600730278","https://openalex.org/W6600812106","https://openalex.org/W6600996794","https://openalex.org/W6603587222"],"related_works":["https://openalex.org/W2734278066","https://openalex.org/W2991844785","https://openalex.org/W2289725842","https://openalex.org/W3153137857","https://openalex.org/W3099674394","https://openalex.org/W2963611087","https://openalex.org/W2498505502","https://openalex.org/W2281241035","https://openalex.org/W2224575773","https://openalex.org/W3105713006","https://openalex.org/W3088654876","https://openalex.org/W3208378969","https://openalex.org/W3206659119","https://openalex.org/W2582609437","https://openalex.org/W2114876173","https://openalex.org/W85558972","https://openalex.org/W2037329184","https://openalex.org/W2050560431","https://openalex.org/W1969028112","https://openalex.org/W1619877374"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}