{"id":"https://openalex.org/W31375011","doi":"https://doi.org/10.3390/s19153387","title":"Fredholm theory in general Banach algebras","display_name":"Fredholm theory in general Banach algebras","publication_year":2010,"publication_date":"2010-03-01","ids":{"openalex":"https://openalex.org/W31375011","doi":"https://doi.org/10.3390/s19153387","mag":"31375011"},"language":"en","primary_location":{"id":"mag:31375011","is_oa":false,"landing_page_url":"https://scholar.sun.ac.za/bitstream/10019.1/4265/1/heymann_fredholm_2010.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors (Basel, Switzerland)","raw_type":null},"type":"dissertation","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10019.1/4265","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011378891","display_name":"Retha Heymann","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Retha Heymann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5011378891"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"15","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":0.9998999834060669,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9998999834060669,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9980999827384949,"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/mathematics","display_name":"Mathematics","score":0.7518655061721802},{"id":"https://openalex.org/keywords/fredholm-operator","display_name":"Fredholm operator","score":0.6957764625549316},{"id":"https://openalex.org/keywords/fredholm-theory","display_name":"Fredholm theory","score":0.5953215956687927},{"id":"https://openalex.org/keywords/compact-operator","display_name":"Compact operator","score":0.504524827003479},{"id":"https://openalex.org/keywords/finite-rank-operator","display_name":"Finite-rank operator","score":0.4900580644607544},{"id":"https://openalex.org/keywords/banach-algebra","display_name":"Banach algebra","score":0.47160086035728455},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4580468535423279},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.4542678892612457},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4470057487487793},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.4372745454311371},{"id":"https://openalex.org/keywords/bounded-operator","display_name":"Bounded operator","score":0.42720139026641846},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4143143892288208},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37155210971832275},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.32084524631500244},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1947513222694397},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.059119194746017456}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7518655061721802},{"id":"https://openalex.org/C2779219991","wikidata":"https://www.wikidata.org/wiki/Q573631","display_name":"Fredholm operator","level":4,"score":0.6957764625549316},{"id":"https://openalex.org/C518188847","wikidata":"https://www.wikidata.org/wiki/Q4455098","display_name":"Fredholm theory","level":4,"score":0.5953215956687927},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.504524827003479},{"id":"https://openalex.org/C99392333","wikidata":"https://www.wikidata.org/wiki/Q5450385","display_name":"Finite-rank operator","level":3,"score":0.4900580644607544},{"id":"https://openalex.org/C2781106287","wikidata":"https://www.wikidata.org/wiki/Q806066","display_name":"Banach algebra","level":3,"score":0.47160086035728455},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4580468535423279},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.4542678892612457},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4470057487487793},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.4372745454311371},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.42720139026641846},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4143143892288208},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37155210971832275},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.32084524631500244},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1947513222694397},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.059119194746017456},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"mag:31375011","is_oa":false,"landing_page_url":"https://scholar.sun.ac.za/bitstream/10019.1/4265/1/heymann_fredholm_2010.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:scholar.sun.ac.za:10019.1/4265","is_oa":true,"landing_page_url":"http://hdl.handle.net/10019.1/4265","pdf_url":"http://hdl.handle.net/10019.1/4265","source":{"id":"https://openalex.org/S4306400300","display_name":"SUNScholar (Stellenbosch University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I26092322","host_organization_name":"Stellenbosch University","host_organization_lineage":["https://openalex.org/I26092322"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis"}],"best_oa_location":{"id":"pmh:oai:scholar.sun.ac.za:10019.1/4265","is_oa":true,"landing_page_url":"http://hdl.handle.net/10019.1/4265","pdf_url":"http://hdl.handle.net/10019.1/4265","source":{"id":"https://openalex.org/S4306400300","display_name":"SUNScholar (Stellenbosch University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I26092322","host_organization_name":"Stellenbosch University","host_organization_lineage":["https://openalex.org/I26092322"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2985019895","display_name":null,"funder_award_id":"51675488","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320327365","display_name":"Ernst and Ethel Eriksen Trust","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W31375011.pdf","grobid_xml":"https://content.openalex.org/works/W31375011.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W316386523","https://openalex.org/W640301599","https://openalex.org/W1505196222","https://openalex.org/W1513637459","https://openalex.org/W1553679168","https://openalex.org/W1569401773","https://openalex.org/W1579129307","https://openalex.org/W1970051016","https://openalex.org/W2017713252","https://openalex.org/W2040884050","https://openalex.org/W2056583468","https://openalex.org/W2064358430","https://openalex.org/W2069095036","https://openalex.org/W2097138469","https://openalex.org/W2107221565","https://openalex.org/W2514271920"],"related_works":["https://openalex.org/W3141497682","https://openalex.org/W2058385170","https://openalex.org/W939494615","https://openalex.org/W2954310368","https://openalex.org/W3197292073","https://openalex.org/W2284797976","https://openalex.org/W2538935172","https://openalex.org/W2501095053","https://openalex.org/W2029373997","https://openalex.org/W2800566713","https://openalex.org/W2088293871","https://openalex.org/W2495418354","https://openalex.org/W2065317404","https://openalex.org/W1470450483","https://openalex.org/W2951277906","https://openalex.org/W2063314199","https://openalex.org/W2052164197","https://openalex.org/W1967876737","https://openalex.org/W2067737135","https://openalex.org/W2955374585"],"abstract_inverted_index":{"Negative-capacitance":[0],"shunted":[1],"piezoelectric":[2,25,73],"polymer":[3],"was":[4],"investigated":[5],"in":[6,36,42,51,159],"depth":[7],"due":[8],"to":[9,79,121,142,147],"its":[10],"considerable":[11],"damping":[12,75,84,170],"effect.":[13],"This":[14,177],"paper":[15],"discusses":[16],"the":[17,60,63,81,87,94,105,115,123,126,135,144,149,154,173],"novel":[18,181],"controlled":[19,183],"stiffness":[20,70,82,102,151,167,184],"performance":[21,171],"from":[22],"a":[23,164,180],"rhombic":[24],"stack":[26],"transducer":[27],"with":[28,38,44,53,161],"three":[29,127],"hybrid":[30,88,128],"negative-impedance":[31],"shunts,":[32],"namely,":[33],"negative":[34,40,47,101,106,136,150,157],"capacitance":[35,41,49,107,137,158],"series":[37,52],"resistance,":[39,45],"parallel":[43,160],"and":[46,72,83,100,108,114,146,169],"inductance/negative":[48],"(NINC)":[50],"resistance.":[54,110],"An":[55],"analytical":[56],"framework":[57],"for":[58,186],"establishing":[59],"model":[61],"of":[62,86,125,153],"coupled":[64],"system":[65],"is":[66],"presented.":[67],"Piezoelectric":[68],"shunt":[69,74],"(PSS)":[71],"(PSD)":[76],"are":[77,119],"proposed":[78],"analyze":[80],"performances":[85],"shunts.":[89,129,176],"Theoretical":[90],"analysis":[91],"proves":[92],"that":[93,134],"PSS":[95],"can":[96],"produce":[97],"both":[98],"positive":[99],"by":[103],"changing":[104],"adjustable":[109],"The":[111,130],"Routh-Hurwitz":[112],"criterion":[113],"root":[116],"locus":[117],"method":[118,185],"utilized":[120],"judge":[122],"stability":[124,145],"results":[131],"point":[132],"out":[133],"should":[138],"be":[139],"selected":[140],"carefully":[141],"sustain":[143],"achieve":[148],"effect":[152],"transducer.":[155],"Furthermore,":[156],"resistance":[162],"has":[163],"considerably":[165],"better":[166],"bandwidth":[168],"than":[172],"other":[174],"two":[175],"study":[178],"demonstrates":[179],"electrically":[182],"vibration":[187],"control":[188],"engineering.":[189]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2025-10-10T17:16:08.811792","created_date":"2025-10-10T00:00:00"}