{"id":"https://openalex.org/W2227575889","doi":null,"title":"Spectral properties of a certain class of Carleman operators","display_name":"Spectral properties of a certain class of Carleman operators","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2227575889","mag":"2227575889"},"language":"en","primary_location":{"id":"pmh:oai:oai.dml.cz:10338.dmlcz/108062","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10338.dmlcz/108062","pdf_url":"http://dml.cz/bitstream/handle/10338.dmlcz/108062/ArchMathRetro_043-2007-3_3.pdf","source":{"id":"https://openalex.org/S4406922294","display_name":"Czech digital mathematics library","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"type:math"},"parent_works":[],"lineage":["https://openalex.org/W2227575889"],"child_works_count":0,"type":"other","is_traditional":false,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://dml.cz/bitstream/handle/10338.dmlcz/108062/ArchMathRetro_043-2007-3_3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089027963","display_name":"S. M. Bahri","orcid":"https://orcid.org/0000-0002-5503-2494","observed_orcids":["https://orcid.org/0000-0002-5503-2494"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S. M. Bahri","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5503-2494","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5089027963"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"043","issue":"3","first_page":"163","last_page":"175"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9945999979972839,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9945999979972839,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.003800000064074993,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.0005000000237487257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/generalized-resolvents","display_name":"generalized resolvents","score":0.9110000133514404},{"id":"https://openalex.org/keywords/symmetric-operators","display_name":"symmetric operators","score":0.7820000052452087},{"id":"https://openalex.org/keywords/resolution-of-identity","display_name":"resolution of the identity","score":0.8259999752044678},{"id":"https://openalex.org/keywords/spectral-theory","display_name":"spectral theory","score":0.3630000054836273},{"id":"https://openalex.org/keywords/hilbert-space-l2","display_name":"Hilbert space l2","score":0.6690000295639038}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8082273602485657},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6643012762069702},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6003221869468689},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5695562362670898},{"id":"https://openalex.org/C167211080","wikidata":"https://www.wikidata.org/wiki/Q285771","display_name":"Riemann\u2013Stieltjes integral","level":3,"score":0.5151745080947876},{"id":"https://openalex.org/C2778740170","wikidata":"https://www.wikidata.org/wiki/Q7575210","display_name":"Spectral space","level":2,"score":0.4288952946662903},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3443293571472168},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32460495829582214},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08742976188659668},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.08372437953948975},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:oai.dml.cz:10338.dmlcz/108062","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10338.dmlcz/108062","pdf_url":"http://dml.cz/bitstream/handle/10338.dmlcz/108062/ArchMathRetro_043-2007-3_3.pdf","source":{"id":"https://openalex.org/S4406922294","display_name":"Czech digital mathematics library","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"type:math"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.482.4958","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.482.4958","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/AM/07-3/am1454.pdf","raw_type":"text"},{"id":"mag:2227575889","doi":null,"is_oa":false,"landing_page_url":"http://emis.maths.adelaide.edu.au/journals/AM/07-3/am1454.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306502959","display_name":"Archivum Mathematicum","issn_l":"0044-8753","issn":["0044-8753","1212-5059"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","ddh","dongbi-c","jufo-1","norway-1","oarl","poland-20","russia-white-list-4"],"host_organization":"https://openalex.org/P4310314295","host_organization_name":"Masaryk University","host_organization_lineage":["https://openalex.org/P4310314295"],"host_organization_lineage_names":["Masaryk University"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Archivum Mathematicum","raw_type":null}],"best_oa_location":{"id":"pmh:oai:oai.dml.cz:10338.dmlcz/108062","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10338.dmlcz/108062","pdf_url":"http://dml.cz/bitstream/handle/10338.dmlcz/108062/ArchMathRetro_043-2007-3_3.pdf","source":{"id":"https://openalex.org/S4406922294","display_name":"Czech digital mathematics library","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"type:math"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2227575889.pdf","grobid_xml":"https://content.openalex.org/works/W2227575889.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W573176839","https://openalex.org/W1896054239","https://openalex.org/W1978939585","https://openalex.org/W1979487140","https://openalex.org/W2008377018","https://openalex.org/W2015967643","https://openalex.org/W2046101549","https://openalex.org/W2047311948","https://openalex.org/W2094553393"],"related_works":["https://openalex.org/W1997238819","https://openalex.org/W2198736319","https://openalex.org/W2056703113","https://openalex.org/W61249772","https://openalex.org/W2022722459","https://openalex.org/W2085218241","https://openalex.org/W2970597235","https://openalex.org/W2056584322","https://openalex.org/W2135910730"],"abstract_inverted_index":{"Abstract.":[0],"The":[1,59,84,243,292],"object":[2],"of":[3,15,19,48,61,64,86,107,129,188,231,239,254,294,309,313,328],"the":[4,11,23,30,35,45,53,104,119,127,148,189,193,213,228,276,297,307,314],"present":[5],"work":[6],"is":[7,41,93,171,184,203,234,248,281,300,305,317],"to":[8,95,103,226,250],"construct":[9],"all":[10],"generalized":[12,46,62,120],"spectral":[13],"functions":[14],"a":[16,65,143,163,185,204,318,334],"certain":[17],"class":[18],"Carleman":[20],"operators":[21,125,331],"in":[22,209,216,296],"Hilbert":[24,144,335],"space":[25,145,336],"L2":[26],"(X,\u00b5)":[27],"and":[28,50,81,153,202,269,304],"establish":[29],"corresponding":[31],"expansion":[32],"theorems,":[33],"when":[34],"deficiency":[36],"indices":[37,71,88,109],"are":[38],"(1,1).":[39],"This":[40],"done":[42],"by":[43,78,136,302],"constructing":[44],"resolvents":[47,63],"A":[49,68,191,255,278,311],"then":[51],"using":[52],"Stieltjes":[54],"inversion":[55],"formula.":[56],"1.":[57],"Preliminaries":[58],"set":[60,230],"symmetric":[66,124],"operator":[67,168,190,206,215,237,277],"with":[69,147],"defect":[70,87,108],"(1,":[72],"1)":[73],"was":[74],"first":[75],"derived":[76],"independently":[77],"Naimark":[79],"[15]":[80],"Krein":[82,96],"[10].":[83],"case":[85,106,128,220],"(m,m),":[89,110],"m":[90,111],"\u2208":[91,112,182,246,261],"N":[92,113],"due":[94],"[11].":[97],"Saakjan":[98],"[19]":[99],"extended":[100],"Krein\u2019s":[101],"formula":[102,122],"general":[105],"\u222a":[114],"{\u221e}.":[115],"In":[116,218,273],"another":[117],"form,":[118],"resolvent":[121,194,229],"for":[123,263],"(including":[126],"non-densely":[130],"defined":[131,165,207],"operators)":[132],"has":[133],"been":[134],"obtained":[135],"Straus":[137],"[20,":[138],"21].":[139],"Let":[140],"H":[141,158,161,210],"be":[142,162,251],"endowed":[146],"inner":[149],"product":[150],"(\u00b7,":[151],"\u00b7),":[152],"let":[154],"A:":[155],"D(A)":[156,262],"\u2282":[157],"\u2212":[159,198,279,287,322],"\u2192":[160],"densely":[164],"closed":[166],"linear":[167],"whose":[169],"range":[170],"denoted":[172,301],"R(A).":[173],"1.1.":[174],"Basic":[175],"Spectral":[176],"Properties.":[177],"We":[178],"say":[179,222],"that":[180,223,339],"\u03bb":[181,224,240,245],"C":[183,247],"regular":[186],"point":[187],"if":[192,256,344],"R\u03bb":[195,233],"=":[196,267,271,290],"(A":[197,286],"\u03bbI)":[199,288],"\u22121":[200],"exists":[201,258],"bounded":[205],"everywhere":[208],"(I":[211],"denotes":[212],"identity":[214,315],"H).":[217],"this":[219,274],"we":[221],"belongs":[225],"\u03c1(A),":[227,295],"A.":[232,310],"an":[235,252,259],"analytic":[236],"function":[238],"on":[241,333],"\u03c1(A).":[242],"number":[244],"said":[249],"eigenvalue":[253],"there":[257],"f":[260,265],"which":[264],"6":[266,289],"0":[268],"Af":[270],"\u03bbf.":[272],"case,":[275],"\u03bbI":[280],"not":[282],"injective,":[283],"i.e.,":[284],"ker":[285],"{0}.":[291],"complement":[293],"complex":[298],"plane,":[299],"\u03c3(A)":[303],"called":[306],"spectrum":[308],"resolution":[312],"[1]":[316],"one-parameter":[319],"family":[320],"{Et},":[321],"\u221e":[323],"<":[324,326],"t":[325,347],"\u221e,":[327],"orthogonal":[329],"projection":[330],"acting":[332],"H,":[337],"such":[338],"i)":[340],"Es":[341],"\u2264":[342,346],"Et":[343],"s":[345],"(monotonicity);":[348]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2016-06-24T00:00:00"}