{"id":"https://openalex.org/W1993783876","doi":"https://doi.org/10.1007/bf02210674","title":"The asymptotic behavior of the eigenvalues and eigenfunctions of the Laplace operator on a compact Riemannian manifold","display_name":"The asymptotic behavior of the eigenvalues and eigenfunctions of the Laplace operator on a compact Riemannian manifold","publication_year":1972,"publication_date":"1972-03-01","ids":{"openalex":"https://openalex.org/W1993783876","doi":"https://doi.org/10.1007/bf02210674","mag":"1993783876"},"language":"en","primary_location":{"id":"doi:10.1007/bf02210674","doi":"https://doi.org/10.1007/bf02210674","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02210674","pdf_url":null,"source":{"id":"https://openalex.org/S143725931","display_name":"Radiophysics and Quantum Electronics","issn_l":"0021-3462","issn":["0021-3462","0033-8443","0097-1545","1573-9120"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Radiophysics and Quantum Electronics","raw_type":"journal-article"},"volume":null,"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/A5059830904","display_name":"V. R. Kogan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V. R. Kogan","raw_affiliation_strings":["Scientific-Research Institute of Applied Mathematics and Cybernetics, Gor'kii University, USSR"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Scientific-Research Institute of Applied Mathematics and Cybernetics, Gor'kii University, USSR","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011033489","display_name":"A. V. Krakhnov","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. V. Krakhnov","raw_affiliation_strings":["Scientific-Research Institute of Applied Mathematics and Cybernetics, Gor'kii University, USSR"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Scientific-Research Institute of Applied Mathematics and Cybernetics, Gor'kii University, USSR","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13411,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"3","first_page":"336","last_page":"340"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9994999766349792,"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":0.9994999766349792,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":9.999999747378752e-05,"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":9.999999747378752e-05,"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/laplacian","display_name":"Laplacian","score":0.9739999771118164},{"id":"https://openalex.org/keywords/compact-riemannian-manifolds","display_name":"compact Riemannian manifolds","score":0.9160000085830688},{"id":"https://openalex.org/keywords/eigenvalues","display_name":"eigenvalues","score":0.5569999814033508},{"id":"https://openalex.org/keywords/eigenfunctions","display_name":"eigenfunctions","score":0.9909999966621399},{"id":"https://openalex.org/keywords/asymptotic-behavior","display_name":"asymptotic behavior","score":0.6959999799728394},{"id":"https://openalex.org/keywords/spectrum","display_name":"spectrum","score":0.550000011920929}],"concepts":[{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.712195634841919},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6548897624015808},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.6437373161315918},{"id":"https://openalex.org/C49747540","wikidata":"https://www.wikidata.org/wiki/Q1071846","display_name":"Laplace\u2013Beltrami operator","level":4,"score":0.6268110871315002},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.6118857860565186},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5915480852127075},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5807071328163147},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.5774795413017273},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5486812591552734},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5439794063568115},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4999527931213379},{"id":"https://openalex.org/C119047807","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.482185035943985},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.4155203700065613},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3386687636375427},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2595766484737396},{"id":"https://openalex.org/C203269682","wikidata":"https://www.wikidata.org/wiki/Q7116898","display_name":"p-Laplacian","level":3,"score":0.18210440874099731},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09489250183105469},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.05739039182662964},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02210674","doi":"https://doi.org/10.1007/bf02210674","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02210674","pdf_url":null,"source":{"id":"https://openalex.org/S143725931","display_name":"Radiophysics and Quantum Electronics","issn_l":"0021-3462","issn":["0021-3462","0033-8443","0097-1545","1573-9120"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Radiophysics and Quantum Electronics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4302419125","https://openalex.org/W2766128145","https://openalex.org/W4300623652","https://openalex.org/W121031341","https://openalex.org/W2038878154","https://openalex.org/W2111271529","https://openalex.org/W2464780829","https://openalex.org/W2963746646","https://openalex.org/W3217737408","https://openalex.org/W2049100000"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-09-21T07:43:02.447757","created_date":"2025-10-10T00:00:00"}