{"id":"https://openalex.org/W4430036","doi":"https://doi.org/10.1007/bf01890607","title":"Causality for nonlinear systems in Hilbert spaces","display_name":"Causality for nonlinear systems in Hilbert spaces","publication_year":1973,"publication_date":"1973-12-01","ids":{"openalex":"https://openalex.org/W4430036","doi":"https://doi.org/10.1007/bf01890607","mag":"4430036"},"language":"en","primary_location":{"id":"doi:10.1007/bf01890607","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01890607","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Mathematical Systems Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076558290","display_name":"Romano M. De Santis","orcid":null},"institutions":[{"id":"https://openalex.org/I45683168","display_name":"Polytechnique Montr\u00e9al","ror":"https://ror.org/05f8d4e86","country_code":"CA","type":"education","lineage":["https://openalex.org/I45683168"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Romano M. Santis","raw_affiliation_strings":["D\u00e9partement de G\u00e9nie \u00c9lectrique, Division d'Automatique \u00c9cole Polytechnique, Montr\u00e9al, Qu\u00e9bec, Canada","D\u00e9partement de G\u00e9nie \u00c9lectrique, Division d'Automatique \u00c9cole Polytechnique, Montr\u00e9al, Canada"],"affiliations":[{"raw_affiliation_string":"D\u00e9partement de G\u00e9nie \u00c9lectrique, Division d'Automatique \u00c9cole Polytechnique, Montr\u00e9al, Qu\u00e9bec, Canada","institution_ids":["https://openalex.org/I45683168"]},{"raw_affiliation_string":"D\u00e9partement de G\u00e9nie \u00c9lectrique, Division d'Automatique \u00c9cole Polytechnique, Montr\u00e9al, Canada","institution_ids":["https://openalex.org/I45683168"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076558290"],"corresponding_institution_ids":["https://openalex.org/I45683168"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.7074,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.89658195,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":"4","first_page":"323","last_page":"337"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.7986000180244446,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.7986000180244446,"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"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.6847000122070312,"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"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.6830000281333923,"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/causality","display_name":"Causality (physics)","score":0.9174973964691162},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6524654626846313},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6358639001846313},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5333065390586853},{"id":"https://openalex.org/keywords/linearity","display_name":"Linearity","score":0.4621703028678894},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4549599885940552},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35278862714767456},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09325012564659119}],"concepts":[{"id":"https://openalex.org/C64357122","wikidata":"https://www.wikidata.org/wiki/Q1149766","display_name":"Causality (physics)","level":2,"score":0.9174973964691162},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6524654626846313},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6358639001846313},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5333065390586853},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.4621703028678894},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4549599885940552},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35278862714767456},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09325012564659119},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01890607","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01890607","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Mathematical Systems Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W152953687","https://openalex.org/W314792534","https://openalex.org/W1969304434","https://openalex.org/W1975447190","https://openalex.org/W1995541787","https://openalex.org/W1999959810","https://openalex.org/W2023311820","https://openalex.org/W2032536668","https://openalex.org/W2045376450","https://openalex.org/W2064054112","https://openalex.org/W2078772200","https://openalex.org/W2092120565","https://openalex.org/W2113369590","https://openalex.org/W4230482343"],"related_works":["https://openalex.org/W2023858428","https://openalex.org/W2126963364","https://openalex.org/W2538259895","https://openalex.org/W2051287254","https://openalex.org/W1489573155","https://openalex.org/W1677090476","https://openalex.org/W2370937376","https://openalex.org/W2081494945","https://openalex.org/W2389053294","https://openalex.org/W1970893504"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-02-25T21:11:00.739837","created_date":"2025-10-10T00:00:00"}