{"id":"https://openalex.org/W7106285866","doi":"https://doi.org/10.48550/arxiv.2511.14979","title":"Transformation from integral operator with separable kernel to matrix in eigenvalue problem","display_name":"Transformation from integral operator with separable kernel to matrix in eigenvalue problem","publication_year":2025,"publication_date":"2025-11-18","ids":{"openalex":"https://openalex.org/W7106285866","doi":"https://doi.org/10.48550/arxiv.2511.14979"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2511.14979","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.14979","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2511.14979","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Hirai, Soma","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hirai, Soma","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Watanabe, Ryoto","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Watanabe, Ryoto","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Nishida, Yuki","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nishida, Yuki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Iwasaki, Masashi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Iwasaki, Masashi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.335999995470047,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.335999995470047,"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"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.09870000183582306,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.07680000364780426,"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6725999712944031},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.659600019454956},{"id":"https://openalex.org/keywords/fourier-integral-operator","display_name":"Fourier integral operator","score":0.6384000182151794},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5928000211715698},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5619999766349792},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.527999997138977},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5242000222206116},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.49149999022483826},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.45500001311302185},{"id":"https://openalex.org/keywords/fredholm-theory","display_name":"Fredholm theory","score":0.4410000145435333}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8084999918937683},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6725999712944031},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.659600019454956},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.6384000182151794},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5928000211715698},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5619999766349792},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.527999997138977},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5242000222206116},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.49149999022483826},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45820000767707825},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.45500001311302185},{"id":"https://openalex.org/C518188847","wikidata":"https://www.wikidata.org/wiki/Q4455098","display_name":"Fredholm theory","level":4,"score":0.4410000145435333},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4374000132083893},{"id":"https://openalex.org/C200052193","wikidata":"https://www.wikidata.org/wiki/Q877802","display_name":"Integral transform","level":2,"score":0.4124999940395355},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.41119998693466187},{"id":"https://openalex.org/C117204833","wikidata":"https://www.wikidata.org/wiki/Q7233207","display_name":"Positive-definite kernel","level":4,"score":0.40549999475479126},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35659998655319214},{"id":"https://openalex.org/C134810832","wikidata":"https://www.wikidata.org/wiki/Q2996956","display_name":"Daniell integral","level":4,"score":0.3443000018596649},{"id":"https://openalex.org/C142017724","wikidata":"https://www.wikidata.org/wiki/Q464118","display_name":"Improper integral","level":4,"score":0.33640000224113464},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.2946999967098236},{"id":"https://openalex.org/C109565186","wikidata":"https://www.wikidata.org/wiki/Q6766437","display_name":"Eigenvalue algorithm","level":5,"score":0.29100000858306885},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27390000224113464},{"id":"https://openalex.org/C165443888","wikidata":"https://www.wikidata.org/wiki/Q1482183","display_name":"Transformation matrix","level":3,"score":0.2676999866962433},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C2776333733","wikidata":"https://www.wikidata.org/wiki/Q3045336","display_name":"Fredholm determinant","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.26260000467300415},{"id":"https://openalex.org/C129683796","wikidata":"https://www.wikidata.org/wiki/Q430450","display_name":"Microlocal analysis","level":4,"score":0.2621999979019165},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C28940832","wikidata":"https://www.wikidata.org/wiki/Q3490774","display_name":"Spectrum of a matrix","level":4,"score":0.25130000710487366}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2511.14979","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.14979","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2511.14979","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.14979","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,29,33,37,42,45,50,54,62,70,81,86],"eigenvalue":[4],"problem":[5],"of":[6,18,21,32,49,56,64,72,75,85],"integral":[7,38,51,66,83],"operators":[8],"whose":[9],"kernels":[10],"can":[11],"be":[12],"expressed":[13],"as":[14],"a":[15,57],"finite":[16],"sum":[17],"pairwise":[19],"products":[20],"single-variable":[22],"functions,":[23],"making":[24],"them":[25],"separable.":[26],"By":[27],"consdiering":[28],"matrix":[30,92],"form":[31],"separable":[34],"kernel":[35],"in":[36],"operator,":[39],"we":[40],"establish":[41],"relationship":[43],"between":[44],"eigenvalues":[46],"and":[47,53,77,94],"eigenfunctions":[48],"operator":[52,67],"eigenpairs":[55,93],"matrix.":[58],"We":[59,97],"next":[60],"generalize":[61],"eigenfunction":[63],"an":[65],"based":[68],"on":[69],"concept":[71],"generalized":[73,95],"eigenvectors":[74],"matrices,":[76],"show":[78],"that":[79],"solving":[80],"Fredholm":[82],"equation":[84],"second":[87],"kind":[88],"reduces":[89],"to":[90,102],"computing":[91],"eigenvectors.":[96],"also":[98],"provide":[99],"several":[100],"examples":[101],"validate":[103],"our":[104],"results.":[105]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-11-23T00:00:00"}