{"id":"https://openalex.org/W2149701817","doi":"https://doi.org/10.1155/2012/843562","title":"On Summability of Spectral Expansions Corresponding to the Sturm-Liouville Operator","display_name":"On Summability of Spectral Expansions Corresponding to the Sturm-Liouville Operator","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2149701817","doi":"https://doi.org/10.1155/2012/843562","mag":"2149701817"},"language":"en","primary_location":{"id":"doi:10.1155/2012/843562","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/843562","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/843562.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2012/843562.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035027648","display_name":"A. S. Makin","orcid":null},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Alexander S. Makin","raw_affiliation_strings":["Moscow State University of Instrument Engineering and Computer Science, Stromynka 20, Moscow 107996, Russia"],"affiliations":[{"raw_affiliation_string":"Moscow State University of Instrument Engineering and Computer Science, Stromynka 20, Moscow 107996, Russia","institution_ids":["https://openalex.org/I19880235"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5035027648"],"corresponding_institution_ids":["https://openalex.org/I19880235"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.2571,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.7773377,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2012","issue":null,"first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":1.0,"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":1.0,"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":0.9987000226974487,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9984999895095825,"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/mathematics","display_name":"Mathematics","score":0.9431470632553101},{"id":"https://openalex.org/keywords/sturm\u2013liouville-theory","display_name":"Sturm\u2013Liouville theory","score":0.8020761013031006},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.7007910013198853},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6214372515678406},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.48310232162475586},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.46909984946250916},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4648837745189667},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4167883098125458},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.35858774185180664}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9431470632553101},{"id":"https://openalex.org/C22892174","wikidata":"https://www.wikidata.org/wiki/Q1154082","display_name":"Sturm\u2013Liouville theory","level":3,"score":0.8020761013031006},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.7007910013198853},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6214372515678406},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.48310232162475586},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46909984946250916},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4648837745189667},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4167883098125458},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.35858774185180664},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2012/843562","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/843562","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/843562.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:843562","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2012/843562.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:06ddc2839a4e4a90b6bd79b6a6e81772","is_oa":true,"landing_page_url":"https://doaj.org/article/06ddc2839a4e4a90b6bd79b6a6e81772","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/843562","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/843562","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/843562.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5997868131","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"}],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2149701817.pdf","grobid_xml":"https://content.openalex.org/works/W2149701817.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W565724841","https://openalex.org/W1489216560","https://openalex.org/W1537906002","https://openalex.org/W1585761266","https://openalex.org/W1802031524","https://openalex.org/W1967318403","https://openalex.org/W1974680369","https://openalex.org/W1976466223","https://openalex.org/W1977143040","https://openalex.org/W1978527244","https://openalex.org/W1978949628","https://openalex.org/W1982421284","https://openalex.org/W1994608784","https://openalex.org/W1996536920","https://openalex.org/W2008887237","https://openalex.org/W2008897700","https://openalex.org/W2013521517","https://openalex.org/W2020185830","https://openalex.org/W2030485955","https://openalex.org/W2039860746","https://openalex.org/W2049589326","https://openalex.org/W2050196536","https://openalex.org/W2054923739","https://openalex.org/W2059061486","https://openalex.org/W2067265108","https://openalex.org/W2068219357","https://openalex.org/W2072056300","https://openalex.org/W2076602752","https://openalex.org/W2078634887","https://openalex.org/W2078868905","https://openalex.org/W2095174761","https://openalex.org/W2951129375","https://openalex.org/W2964029667","https://openalex.org/W2990934340","https://openalex.org/W3021722416","https://openalex.org/W3040370491","https://openalex.org/W4230100213","https://openalex.org/W4230379347","https://openalex.org/W4247178975","https://openalex.org/W4247679684","https://openalex.org/W4256624880"],"related_works":["https://openalex.org/W1042862008","https://openalex.org/W2775543732","https://openalex.org/W2609569092","https://openalex.org/W2560305623","https://openalex.org/W1889741107","https://openalex.org/W2361328826","https://openalex.org/W2076229781","https://openalex.org/W2070132034","https://openalex.org/W1649046395","https://openalex.org/W2384439970"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,6,10,15,20],"completeness":[3],"property":[4,8],"and":[5],"basis":[7],"of":[9,14,27],"root":[11],"function":[12],"system":[13],"Sturm-Liouville":[16],"operator":[17],"defined":[18],"on":[19],"segment":[21],"[0,":[22],"1].":[23],"All":[24],"possible":[25],"types":[26],"two-point":[28],"boundary":[29],"conditions":[30],"are":[31],"considered.":[32]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
