{"id":"https://openalex.org/W2139536989","doi":"https://doi.org/10.1142/s0218127403007758","title":"On Subordination of Convolution Semigroups","display_name":"On Subordination of Convolution Semigroups","publication_year":2003,"publication_date":"2003-07-01","ids":{"openalex":"https://openalex.org/W2139536989","doi":"https://doi.org/10.1142/s0218127403007758","mag":"2139536989"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127403007758","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127403007758","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5084476700","display_name":"Sonia Ben Othman","orcid":"https://orcid.org/0009-0002-3337-3391"},"institutions":[{"id":"https://openalex.org/I108714496","display_name":"Tunis University","ror":"https://ror.org/02q1spa57","country_code":"TN","type":"education","lineage":["https://openalex.org/I108714496"]}],"countries":["TN"],"is_corresponding":true,"raw_author_name":"Sonia Ben Othman","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques, Facult\u00e9 des Sciences de Tunis, TN-1060 Tunis, Tunisia"],"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques, Facult\u00e9 des Sciences de Tunis, TN-1060 Tunis, Tunisia","institution_ids":["https://openalex.org/I108714496"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038463921","display_name":"Slim Bouaziz","orcid":null},"institutions":[{"id":"https://openalex.org/I108714496","display_name":"Tunis University","ror":"https://ror.org/02q1spa57","country_code":"TN","type":"education","lineage":["https://openalex.org/I108714496"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Slim Bouaziz","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques, Facult\u00e9 des Sciences de Tunis, TN-1060 Tunis, Tunisia"],"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques, Facult\u00e9 des Sciences de Tunis, TN-1060 Tunis, Tunisia","institution_ids":["https://openalex.org/I108714496"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031456735","display_name":"Mohamed Hmissi","orcid":"https://orcid.org/0000-0002-1994-8024"},"institutions":[{"id":"https://openalex.org/I108714496","display_name":"Tunis University","ror":"https://ror.org/02q1spa57","country_code":"TN","type":"education","lineage":["https://openalex.org/I108714496"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Mohamed Hmissi","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques, Facult\u00e9 des Sciences de Tunis, TN-1060 Tunis, Tunisia"],"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques, Facult\u00e9 des Sciences de Tunis, TN-1060 Tunis, Tunisia","institution_ids":["https://openalex.org/I108714496"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5084476700"],"corresponding_institution_ids":["https://openalex.org/I108714496"],"apc_list":null,"apc_paid":null,"fwci":0.8094,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.8031651,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"07","first_page":"1917","last_page":"1922"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9684000015258789,"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"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9684000015258789,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9660999774932861,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9546999931335449,"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/subordinator","display_name":"Subordinator","score":0.8653051853179932},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.8308363556861877},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7851276397705078},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.7405978441238403},{"id":"https://openalex.org/keywords/subordination","display_name":"Subordination (linguistics)","score":0.6876689195632935},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6729066371917725},{"id":"https://openalex.org/keywords/lebesgue-measure","display_name":"Lebesgue measure","score":0.6414909958839417},{"id":"https://openalex.org/keywords/borel-measure","display_name":"Borel measure","score":0.6226722002029419},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5155701041221619},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4509741961956024},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41794553399086},{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.22247770428657532},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.18622726202011108},{"id":"https://openalex.org/keywords/l\u00e9vy-process","display_name":"L\u00e9vy process","score":0.18338444828987122},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.12145641446113586},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05599009990692139}],"concepts":[{"id":"https://openalex.org/C2781362121","wikidata":"https://www.wikidata.org/wiki/Q7631785","display_name":"Subordinator","level":3,"score":0.8653051853179932},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.8308363556861877},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7851276397705078},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.7405978441238403},{"id":"https://openalex.org/C2777406531","wikidata":"https://www.wikidata.org/wiki/Q2031017","display_name":"Subordination (linguistics)","level":2,"score":0.6876689195632935},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6729066371917725},{"id":"https://openalex.org/C2777105136","wikidata":"https://www.wikidata.org/wiki/Q827230","display_name":"Lebesgue measure","level":3,"score":0.6414909958839417},{"id":"https://openalex.org/C166758865","wikidata":"https://www.wikidata.org/wiki/Q892585","display_name":"Borel measure","level":3,"score":0.6226722002029419},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5155701041221619},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4509741961956024},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41794553399086},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.22247770428657532},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.18622726202011108},{"id":"https://openalex.org/C88757350","wikidata":"https://www.wikidata.org/wiki/Q1557613","display_name":"L\u00e9vy process","level":2,"score":0.18338444828987122},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.12145641446113586},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05599009990692139},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127403007758","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127403007758","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.550000011920929}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W103694324","https://openalex.org/W1527296550","https://openalex.org/W1973047506","https://openalex.org/W1983712173","https://openalex.org/W2077267175"],"related_works":["https://openalex.org/W3216788528","https://openalex.org/W4297789184","https://openalex.org/W3108160348","https://openalex.org/W2950462082","https://openalex.org/W2084273165","https://openalex.org/W2963005874","https://openalex.org/W2059279463","https://openalex.org/W2613481088","https://openalex.org/W4245983123","https://openalex.org/W3021345697"],"abstract_inverted_index":{"Let":[0,22,49],"\u03bc":[1,38,107,117,147],":=":[2,82],"(\u03bc":[3],"t":[4,6,39,46,81],")":[5,170],"&gt;":[7,47],"0":[8],"be":[9,24,51,101,109],"a":[10,119,129],"convolution":[11,111,130],"semigroup":[12,112,131],"on":[13,33,132],"\u211d":[14,34,68],"d":[15,35,69],"endowed":[16],"with":[17,103],"its":[18],"Lebesgue":[19],"measure":[20,174],"\u03bb.":[21],"\u2133(\u03bc)":[23,164],"the":[25,52,75,110,172,178],"set":[26,53,61],"of":[27,54,58,62,116,146,155],"all":[28,55],"positive":[29],"Borel":[30,63],"measures":[31],"\u03c9":[32,41,161,166],"for":[36,44],"which":[37,73],"*":[40],"\u226a":[42],"\u03bb,":[43],"each":[45],"0.":[48],"EX(\u03bc)":[50,99],"exit":[56,143,153],"laws":[57],"\u03bc,":[59,156],"i.e.the":[60],"functions":[64],"\u03c6":[65,80],":]0,":[66],"\u221e[\u00d7":[67],"\u21a6":[70],"[0,":[71],"\u221e]":[72],"verifies":[74],"functional":[76],"equation":[77],"(by":[78],"putting":[79],"\u03c6(t,":[83],".))":[84],"[Formula:":[85,123],"see":[86,124],"text]":[87,125],"Under":[88],"some":[89,152],"\u03bb-regularity":[90],"assumptions,":[91],"it":[92],"is":[93,128,135,149,171],"proved":[94,137],"in":[95,138],"this":[96,139],"paper":[97,140],"that":[98],"can":[100],"identified":[102],"\u2133(\u03bc).":[104],"Moreover,":[105],"let":[106],"\u03b2":[108,121,127,148,169],"obtained":[113],"by":[114,118,177],"subordination":[115],"subordinator":[120],"(i.e.":[122],"where":[126,165],"[0,\u221e[).":[133],"It":[134],"also":[136],"that,":[141],"an":[142],"law":[144,154],"\u03c8":[145,176],"subordinated":[150],"to":[151,163,175],"if":[157,160],"and":[158],"only":[159],"belongs":[162],"\u2208":[167],"\u2133(\u03bc":[168],"associated":[173],"preceding":[179],"identification.":[180]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
