{"id":"https://openalex.org/W3209535653","doi":"https://doi.org/10.3390/math9212738","title":"Basic Fundamental Formulas for Wiener Transforms Associated with a Pair of Operators on Hilbert Space","display_name":"Basic Fundamental Formulas for Wiener Transforms Associated with a Pair of Operators on Hilbert Space","publication_year":2021,"publication_date":"2021-10-28","ids":{"openalex":"https://openalex.org/W3209535653","doi":"https://doi.org/10.3390/math9212738","mag":"3209535653"},"language":"en","primary_location":{"id":"doi:10.3390/math9212738","doi":"https://doi.org/10.3390/math9212738","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/math9212738","pdf_url":"https://www.mdpi.com/2227-7390/9/21/2738/pdf?version=1635756459","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2227-7390/9/21/2738/pdf?version=1635756459","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058475025","display_name":"Hyun Soo Chung","orcid":"https://orcid.org/0000-0003-1458-7087","observed_orcids":["https://orcid.org/0000-0003-1458-7087"]},"institutions":[{"id":"https://openalex.org/I89015989","display_name":"Dankook University","ror":"https://ror.org/058pdbn81","country_code":"KR","type":"education","lineage":["https://openalex.org/I89015989"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Hyun Chung","raw_affiliation_strings":["Department of Mathematics, Dankook University, Cheonan 31116, Korea"],"raw_orcid":"https://orcid.org/0000-0003-1458-7087","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Dankook University, Cheonan 31116, Korea","institution_ids":["https://openalex.org/I89015989"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058475025"],"corresponding_institution_ids":["https://openalex.org/I89015989"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1728},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1728},"fwci":0.2089,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.3167219,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":"9","issue":"21","first_page":"2738","last_page":"2738"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.8690999746322632,"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"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.8690999746322632,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.05829999968409538,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.01850000023841858,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hilbert-space-operators","display_name":"Hilbert space operators","score":0.7350000143051147},{"id":"https://openalex.org/keywords/inversion-formula","display_name":"inversion formula","score":0.6269999742507935},{"id":"https://openalex.org/keywords/composition-formulas","display_name":"composition formulas","score":0.8169999718666077},{"id":"https://openalex.org/keywords/segal","display_name":"Segal","score":0.4860000014305115},{"id":"https://openalex.org/keywords/hida","display_name":"Hida","score":0.7379999756813049}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7672713398933411},{"id":"https://openalex.org/C27219502","wikidata":"https://www.wikidata.org/wiki/Q6777133","display_name":"Integral representation theorem for classical Wiener space","level":4,"score":0.6912165284156799},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6072974801063538},{"id":"https://openalex.org/C89451469","wikidata":"https://www.wikidata.org/wiki/Q1443036","display_name":"Parseval's theorem","level":5,"score":0.6051912307739258},{"id":"https://openalex.org/C178166229","wikidata":"https://www.wikidata.org/wiki/Q5128316","display_name":"Classical Wiener space","level":3,"score":0.5813416242599487},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5366679430007935},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5255205631256104},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.5225555300712585},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4195067584514618},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3675945997238159},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.24060645699501038},{"id":"https://openalex.org/C60391097","wikidata":"https://www.wikidata.org/wiki/Q1056809","display_name":"Wiener process","level":2,"score":0.16663581132888794},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.12850654125213623},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.1156061589717865},{"id":"https://openalex.org/C101812284","wikidata":"https://www.wikidata.org/wiki/Q2450135","display_name":"Functional integration","level":3,"score":0.0642579197883606}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/math9212738","doi":"https://doi.org/10.3390/math9212738","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/math9212738","pdf_url":"https://www.mdpi.com/2227-7390/9/21/2738/pdf?version=1635756459","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:gam:jmathe:v:9:y:2021:i:21:p:2738-:d:666805","doi":null,"is_oa":false,"landing_page_url":"https://www.mdpi.com/2227-7390/9/21/2738/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:23858e7822274af88cd0ecbe5e3f0afa","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/23858e7822274af88cd0ecbe5e3f0afa","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics, Vol 9, Iss 21, p 2738 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/math9212738","doi":"https://doi.org/10.3390/math9212738","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/math9212738","pdf_url":"https://www.mdpi.com/2227-7390/9/21/2738/pdf?version=1635756459","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3209535653.pdf","grobid_xml":"https://content.openalex.org/works/W3209535653.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1966296504","https://openalex.org/W1983157321","https://openalex.org/W1984285783","https://openalex.org/W2000243721","https://openalex.org/W2027705744","https://openalex.org/W2077988269","https://openalex.org/W2124801739","https://openalex.org/W2158303775","https://openalex.org/W2259441849","https://openalex.org/W2319134735","https://openalex.org/W3014534335","https://openalex.org/W3150376588","https://openalex.org/W4237415092"],"related_works":["https://openalex.org/W1984285783","https://openalex.org/W2077988269","https://openalex.org/W4285223555","https://openalex.org/W1991125177","https://openalex.org/W7166303640","https://openalex.org/W1966296504","https://openalex.org/W2013099281","https://openalex.org/W2981967661","https://openalex.org/W2090231704","https://openalex.org/W2081866116"],"abstract_inverted_index":{"Segal":[0,86],"introduce":[1],"the":[2,6,23,38,40,43,47,51,62,68,76,96],"Fourier\u2013Wiener":[3],"transform":[4,26,78],"for":[5,50,61,75],"class":[7],"of":[8,98],"polynomial":[9],"cylinder":[10],"functions":[11],"on":[12],"Hilbert":[13],"space,":[14],"and":[15,46,82,87],"Hida":[16],"then":[17,94],"develop":[18],"this":[19,66],"concept.":[20],"Negrin":[21],"define":[22],"extended":[24],"Wiener":[25,52,63,77],"with":[27],"Hayker":[28,34,90],"et":[29,35,91],"al.":[30,36,92],"In":[31,65],"recent":[32],"papers,":[33],"establish":[37,58],"existence,":[39],"composition":[41],"formula,":[42,45],"inversion":[44],"Parseval":[48],"relation":[49],"transform.":[53,64],"But,":[54],"they":[55],"do":[56],"not":[57],"homomorphism":[59],"properties":[60],"paper,":[67],"author":[69],"establishes":[70],"some":[71,80,103],"basic":[72,99],"fundamental":[73,100],"formulas":[74,101],"via":[79],"concepts":[81],"motivations":[83],"introduced":[84],"by":[85,89],"used":[88],"We":[93],"state":[95],"usefulness":[97],"as":[102],"applications.":[104]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-10-27T15:51:10.671819","created_date":"2021-11-08T00:00:00"}