{"id":"https://openalex.org/W2039267170","doi":"https://doi.org/10.1137/130922215","title":"The Interior Transmission Problem: Spectral Theory","display_name":"The Interior Transmission Problem: Spectral Theory","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2039267170","doi":"https://doi.org/10.1137/130922215","mag":"2039267170"},"language":"en","primary_location":{"id":"doi:10.1137/130922215","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130922215","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108417533","display_name":"M. Faierman","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Melvin Faierman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5108417533"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8994,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.93021829,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"46","issue":"1","first_page":"803","last_page":"819"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9994000196456909,"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":0.8521159887313843},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6673619747161865},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5562931895256042},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5488784909248352},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5301170349121094},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5175284743309021},{"id":"https://openalex.org/keywords/spectral-theory","display_name":"Spectral theory","score":0.4901476800441742},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.4775339365005493},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.47266635298728943},{"id":"https://openalex.org/keywords/quadratic-form","display_name":"Quadratic form (statistics)","score":0.4269615113735199},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.4147789478302002},{"id":"https://openalex.org/keywords/operator-matrix","display_name":"Operator matrix","score":0.41408300399780273},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.410089373588562},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3438054919242859},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23646271228790283},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08588641881942749}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8521159887313843},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6673619747161865},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5562931895256042},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5488784909248352},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5301170349121094},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5175284743309021},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.4901476800441742},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4775339365005493},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47266635298728943},{"id":"https://openalex.org/C152022596","wikidata":"https://www.wikidata.org/wiki/Q7268361","display_name":"Quadratic form (statistics)","level":2,"score":0.4269615113735199},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.4147789478302002},{"id":"https://openalex.org/C2992500303","wikidata":"https://www.wikidata.org/wiki/Q5680845","display_name":"Operator matrix","level":2,"score":0.41408300399780273},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.410089373588562},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3438054919242859},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23646271228790283},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08588641881942749},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130922215","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130922215","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1532154335","https://openalex.org/W1575147392","https://openalex.org/W1580390795","https://openalex.org/W1971695334","https://openalex.org/W1981942999","https://openalex.org/W2007334673","https://openalex.org/W2026498853","https://openalex.org/W2028472808","https://openalex.org/W2036249610","https://openalex.org/W2041390660","https://openalex.org/W2041502917","https://openalex.org/W2049557728","https://openalex.org/W2058875971","https://openalex.org/W2062462246","https://openalex.org/W2065182779","https://openalex.org/W2077355015","https://openalex.org/W2079622531","https://openalex.org/W2125404669","https://openalex.org/W2334378917","https://openalex.org/W2564269316","https://openalex.org/W2962742655","https://openalex.org/W2963662079","https://openalex.org/W3106219116","https://openalex.org/W3106447845","https://openalex.org/W4237085618"],"related_works":["https://openalex.org/W2091702770","https://openalex.org/W2963107861","https://openalex.org/W2962943990","https://openalex.org/W1987371078","https://openalex.org/W2964117276","https://openalex.org/W2962743232","https://openalex.org/W2041390660","https://openalex.org/W2020695975","https://openalex.org/W1991943387","https://openalex.org/W1968702268","https://openalex.org/W1765093622","https://openalex.org/W2330304929","https://openalex.org/W3168214540","https://openalex.org/W3006186534","https://openalex.org/W3106265920","https://openalex.org/W2952871818","https://openalex.org/W3049021005","https://openalex.org/W2743034393","https://openalex.org/W2165842171","https://openalex.org/W2620903817"],"abstract_inverted_index":{"In":[0],"this":[1,36],"paper":[2],"we":[3,51,75,86,124,148],"are":[4,52],"concerned":[5],"with":[6,13,18],"the":[7,30,46,63,69,78,91,101,105,112,128,142,145,156,166],"interior":[8,167],"transmission":[9,168],"eigenvalue":[10],"problem":[11,17,59,81,169],"connected":[12],"a":[14,120],"degenerate":[15],"boundary":[16,37,58,80,114],"limited":[19],"smoothness":[20],"assumptions":[21,74],"concerning":[22,45,93],"its":[23],"coefficients":[24],"and":[25,84],"boundary.":[26],"If":[27],"$\\mathcal{A}_2$":[28,117,161],"denotes":[29],"Hilbert":[31],"space":[32],"operator":[33,107],"induced":[34,110],"by":[35,111,134],"problem,":[38,147],"then":[39],"in":[40],"order":[41],"to":[42,54,68,90,96,100,136,141],"derive":[43,97],"information":[44,98],"spectral":[47,64,102,129,157],"properties":[48,103,130],"of":[49,62,104,122,131,144],"$\\mathcal{A}_2$,":[50],"led":[53],"consider":[55],"an":[56],"auxiliary":[57,79,113],"involving":[60],"powers":[61],"parameter":[65],"$\\lambda$":[66],"up":[67],"second":[70],"order.":[71],"Under":[72],"our":[73],"show":[76,149],"that":[77,150,164],"is":[82,118,162],"parameter-elliptic,":[83],"hence":[85],"can":[87],"now":[88],"appeal":[89],"theory":[92,158],"such":[94],"problems":[95],"pertaining":[99,140],"quadratic":[106],"pencil":[108],"$V_2(\\lambda)$":[109],"problem.":[115],"Since":[116],"just":[119],"linearization":[121],"$V_2(\\lambda)$,":[123],"thus":[125],"arrive":[126],"at":[127],"$\\mathcal{A}_2$.":[132],"Finally,":[133],"appealing":[135],"some":[137,153],"known":[138],"results":[139],"uniqueness":[143],"Cauchy":[146],"under":[151,170],"possibly":[152],"further":[154],"conditions,":[155],"derived":[159],"for":[160,165],"precisely":[163],"consideration.":[171]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}