{"id":"https://openalex.org/W4317543803","doi":"https://doi.org/10.1137/22m1486157","title":"The Weyl Law of Transmission Eigenvalues and the Completeness of Generalized Transmission Eigenfunctions without Complementing Conditions","display_name":"The Weyl Law of Transmission Eigenvalues and the Completeness of Generalized Transmission Eigenfunctions without Complementing Conditions","publication_year":2023,"publication_date":"2023-08-22","ids":{"openalex":"https://openalex.org/W4317543803","doi":"https://doi.org/10.1137/22m1486157"},"language":"en","primary_location":{"id":"doi:10.1137/22m1486157","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1486157","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/309692","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005843048","display_name":"Jean Fornerod","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Jean Fornerod","raw_affiliation_strings":["Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, EPFL, SB, GR-PI, Station 8, CH-1015 Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, EPFL, SB, GR-PI, Station 8, CH-1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078018452","display_name":"Ho\u00e0i-Minh Nguy\u00ean","orcid":"https://orcid.org/0000-0002-5690-6026"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Hoai-Minh Nguyen","raw_affiliation_strings":["Laboratoire Jacques Louis Lions, Sorbonne Universit\u00e9, 75252, Paris, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques Louis Lions, Sorbonne Universit\u00e9, 75252, Paris, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005843048"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":3.193,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.91507799,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"55","issue":"4","first_page":"3959","last_page":"3999"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9998000264167786,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9998000264167786,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9995999932289124,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8600536584854126},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.762671172618866},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.7265859246253967},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.661941409111023},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5893704295158386},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5720245838165283},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.5408279299736023},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.5270331501960754},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4986269474029541},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39400944113731384},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07004308700561523}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8600536584854126},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.762671172618866},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.7265859246253967},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.661941409111023},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5893704295158386},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5720245838165283},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.5408279299736023},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.5270331501960754},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4986269474029541},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39400944113731384},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07004308700561523},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/22m1486157","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1486157","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:309692","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/309692","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WoS","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:309692","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/309692","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WoS","raw_type":"research article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W1532154335","https://openalex.org/W1539361036","https://openalex.org/W1545761024","https://openalex.org/W1586623601","https://openalex.org/W1855543705","https://openalex.org/W1866311589","https://openalex.org/W1971870342","https://openalex.org/W1981262314","https://openalex.org/W1985697506","https://openalex.org/W1987371078","https://openalex.org/W1987644927","https://openalex.org/W1991943387","https://openalex.org/W2004096326","https://openalex.org/W2007334673","https://openalex.org/W2020695975","https://openalex.org/W2028472808","https://openalex.org/W2032554443","https://openalex.org/W2041390660","https://openalex.org/W2041502917","https://openalex.org/W2073370369","https://openalex.org/W2268819650","https://openalex.org/W2479078586","https://openalex.org/W2494193511","https://openalex.org/W2527953407","https://openalex.org/W2543300175","https://openalex.org/W2573858862","https://openalex.org/W2587376768","https://openalex.org/W2962742655","https://openalex.org/W2962844355","https://openalex.org/W2962943990","https://openalex.org/W2963220760","https://openalex.org/W2963266935","https://openalex.org/W2963379440","https://openalex.org/W2963783511","https://openalex.org/W2964117276","https://openalex.org/W2976067063","https://openalex.org/W3043012630","https://openalex.org/W3099015552","https://openalex.org/W3106447845","https://openalex.org/W3129093488","https://openalex.org/W3154509926","https://openalex.org/W3162757862","https://openalex.org/W3171000776","https://openalex.org/W3173198119","https://openalex.org/W3181369870","https://openalex.org/W4229590639","https://openalex.org/W4231706539","https://openalex.org/W4242473853","https://openalex.org/W4243738351","https://openalex.org/W4245183679"],"related_works":["https://openalex.org/W2245403906","https://openalex.org/W2393344178","https://openalex.org/W2495930062","https://openalex.org/W2051796801","https://openalex.org/W2057370678","https://openalex.org/W2794789911","https://openalex.org/W2353039109","https://openalex.org/W4206553170","https://openalex.org/W1971695127","https://openalex.org/W1666863754"],"abstract_inverted_index":{"The":[0],"transmission":[1],"eigenvalue":[2],"problem":[3],"is":[4,88],"a":[5,42,100,103,130],"system":[6,43,53],"of":[7,12,37,51,78,82,85,126],"two":[8,13,49],"second-order":[9,60,118],"elliptic":[10],"equations":[11,50],"unknowns":[14],"equipped":[15],"with":[16],"the":[17,21,28,32,35,38,48,52,55,59,83,86,91,94,114,117],"Cauchy":[18],"data":[19],"on":[20],"boundary.":[22],"In":[23],"this":[24],"work,":[25],"we":[26,105],"establish":[27,90],"Weyl":[29],"law":[30],"for":[31,41,58,98,112,116],"eigenvalues":[33],"and":[34,62,73,93,108,125],"completeness":[36],"generalized":[39],"eigenfunctions":[40],"without":[44],"complementing":[45],"conditions,":[46],"i.e.,":[47],"have":[54],"same":[56],"coefficients":[57,67,115],"terms,":[61],"thus":[63],"being":[64],"degenerate.":[65],"These":[66],"are":[68,74,120],"allowed":[69],"to":[70,76,89,122],"be":[71,77,123],"anisotropic":[72],"assumed":[75],"class":[79,127],"C2.":[80],"One":[81],"keys":[84],"analysis":[87],"well-posedness":[92],"regularity":[95],"in":[96],"Lp-scale":[97],"such":[99],"system.":[101],"As":[102],"result,":[104],"largely":[106],"extend":[107],"rediscover":[109],"known":[110],"results":[111],"which":[113],"terms":[119],"required":[121],"isotropic":[124],"C\\\\infty":[128],"using":[129],"new":[131],"approach.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-04-11T08:14:18.477133","created_date":"2025-10-10T00:00:00"}