{"id":"https://openalex.org/W4220776599","doi":"https://doi.org/10.3390/sym14030557","title":"The Spectrum of Second Order Quantum Difference Operator","display_name":"The Spectrum of Second Order Quantum Difference Operator","publication_year":2022,"publication_date":"2022-03-10","ids":{"openalex":"https://openalex.org/W4220776599","doi":"https://doi.org/10.3390/sym14030557"},"language":"en","primary_location":{"id":"doi:10.3390/sym14030557","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14030557","pdf_url":"https://www.mdpi.com/2073-8994/14/3/557/pdf?version=1646970714","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/3/557/pdf?version=1646970714","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053611401","display_name":"Taja Yaying","orcid":"https://orcid.org/0000-0003-3435-8417"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Taja Yaying","raw_affiliation_strings":["Department of Mathematics, Dera Natung Government College, Itanagar 791113, India"],"raw_orcid":"https://orcid.org/0000-0003-3435-8417","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Dera Natung Government College, Itanagar 791113, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030425660","display_name":"Bipan Hazarika","orcid":"https://orcid.org/0000-0002-0644-0600"},"institutions":[{"id":"https://openalex.org/I138537684","display_name":"Gauhati University","ror":"https://ror.org/01ppj9r51","country_code":"IN","type":"education","lineage":["https://openalex.org/I138537684"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Bipan Hazarika","raw_affiliation_strings":["Department of Mathematics, Gauhati University, Gauhati 781014, India"],"raw_orcid":"https://orcid.org/0000-0002-0644-0600","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Gauhati University, Gauhati 781014, India","institution_ids":["https://openalex.org/I138537684"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019797810","display_name":"Binod Chandra Tripathy","orcid":"https://orcid.org/0000-0002-0738-652X"},"institutions":[{"id":"https://openalex.org/I72677176","display_name":"Tripura University","ror":"https://ror.org/05xqycm14","country_code":"IN","type":"education","lineage":["https://openalex.org/I72677176"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Binod Chandra Tripathy","raw_affiliation_strings":["Department of Mathematics, Tripura University, Agartala 799022, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tripura University, Agartala 799022, India","institution_ids":["https://openalex.org/I72677176"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102867027","display_name":"M. \u200eMursaleen","orcid":"https://orcid.org/0000-0003-4128-0427"},"institutions":[{"id":"https://openalex.org/I171210897","display_name":"Aligarh Muslim University","ror":"https://ror.org/03kw9gc02","country_code":"IN","type":"education","lineage":["https://openalex.org/I171210897"]},{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]},{"id":"https://openalex.org/I4210126829","display_name":"China Medical University Hospital","ror":"https://ror.org/0368s4g32","country_code":"TW","type":"healthcare","lineage":["https://openalex.org/I4210126829"]}],"countries":["IN","TW"],"is_corresponding":true,"raw_author_name":"Mohammad Mursaleen","raw_affiliation_strings":["Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India","Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung 40001, Taiwan"],"raw_orcid":"https://orcid.org/0000-0003-4128-0427","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India","institution_ids":["https://openalex.org/I171210897"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung 40001, Taiwan","institution_ids":["https://openalex.org/I4210126829","https://openalex.org/I184693016"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5102867027"],"corresponding_institution_ids":["https://openalex.org/I171210897","https://openalex.org/I184693016","https://openalex.org/I4210126829"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.7249,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.94361608,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"14","issue":"3","first_page":"557","last_page":"557"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9854000210762024,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9599000215530396,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7780415415763855},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.7094386219978333},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5972819328308105},{"id":"https://openalex.org/keywords/finite-rank-operator","display_name":"Finite-rank operator","score":0.5198043584823608},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4969816505908966},{"id":"https://openalex.org/keywords/pseudo-monotone-operator","display_name":"Pseudo-monotone operator","score":0.49027517437934875},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.4749327301979065},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4143403172492981},{"id":"https://openalex.org/keywords/compact-operator","display_name":"Compact operator","score":0.4101567268371582},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.3711484670639038},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3249104917049408},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27684420347213745},{"id":"https://openalex.org/keywords/operator-space","display_name":"Operator space","score":0.22587773203849792},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12331292033195496},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11280450224876404},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06929770112037659}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7780415415763855},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.7094386219978333},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5972819328308105},{"id":"https://openalex.org/C99392333","wikidata":"https://www.wikidata.org/wiki/Q5450385","display_name":"Finite-rank operator","level":3,"score":0.5198043584823608},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4969816505908966},{"id":"https://openalex.org/C201040074","wikidata":"https://www.wikidata.org/wiki/Q7254436","display_name":"Pseudo-monotone operator","level":5,"score":0.49027517437934875},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.4749327301979065},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4143403172492981},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.4101567268371582},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.3711484670639038},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3249104917049408},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27684420347213745},{"id":"https://openalex.org/C176691602","wikidata":"https://www.wikidata.org/wiki/Q7097841","display_name":"Operator space","level":4,"score":0.22587773203849792},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12331292033195496},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11280450224876404},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06929770112037659},{"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/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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"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:10.3390/sym14030557","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14030557","pdf_url":"https://www.mdpi.com/2073-8994/14/3/557/pdf?version=1646970714","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:fff8a05e39ef438a8b1c64d000c448d6","is_oa":true,"landing_page_url":"https://doaj.org/article/fff8a05e39ef438a8b1c64d000c448d6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 3, p 557 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/3/557/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14030557","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14030557","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14030557","pdf_url":"https://www.mdpi.com/2073-8994/14/3/557/pdf?version=1646970714","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2671152974","display_name":null,"funder_award_id":"EEQ/2019/000082","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G8779551006","display_name":null,"funder_award_id":"EEQ/2019/000082","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"}],"funders":[{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"},{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4220776599.pdf","grobid_xml":"https://content.openalex.org/works/W4220776599.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W25297749","https://openalex.org/W1972975475","https://openalex.org/W1975495390","https://openalex.org/W1982622831","https://openalex.org/W1988135709","https://openalex.org/W2019115866","https://openalex.org/W2019317216","https://openalex.org/W2031484954","https://openalex.org/W2038892837","https://openalex.org/W2068838874","https://openalex.org/W2069837708","https://openalex.org/W2091727114","https://openalex.org/W2096083408","https://openalex.org/W2166604581","https://openalex.org/W2182444765","https://openalex.org/W2210404839","https://openalex.org/W2300479239","https://openalex.org/W2318423024","https://openalex.org/W2897922906","https://openalex.org/W2954158163","https://openalex.org/W3027302360","https://openalex.org/W3047144032","https://openalex.org/W3080489491","https://openalex.org/W3093997535","https://openalex.org/W3096258866","https://openalex.org/W3099108074","https://openalex.org/W3120330753","https://openalex.org/W3123478602","https://openalex.org/W3164715920","https://openalex.org/W3164931090","https://openalex.org/W3201707793","https://openalex.org/W4237067428","https://openalex.org/W4240644230","https://openalex.org/W6677991024"],"related_works":["https://openalex.org/W2202672589","https://openalex.org/W3175776911","https://openalex.org/W2039272528","https://openalex.org/W2990293054","https://openalex.org/W2092933505","https://openalex.org/W4246967054","https://openalex.org/W2387027204","https://openalex.org/W2171801330","https://openalex.org/W2469762381","https://openalex.org/W2384142831"],"abstract_inverted_index":{"In":[0],"this":[1],"study,":[2],"we":[3],"give":[4],"another":[5],"generalization":[6],"of":[7,42,95,104],"second":[8],"order":[9],"backward":[10],"difference":[11],"operator":[12,21,97],"\u22072":[13],"by":[14],"introducing":[15],"its":[16,31],"quantum":[17],"analog":[18],"\u2207q2.":[19],"The":[20],"\u2207q2":[22,98],"represents":[23],"the":[24,37,51,78,83,85,88,92,96,100],"third":[25],"band":[26],"infinite":[27],"matrix.":[28],"We":[29,76],"construct":[30],"domains":[32,52],"c0(\u2207q2)":[33,53],"and":[34,40,44,48,54,63,66,71,74,91],"c(\u2207q2)":[35,55],"in":[36],"spaces":[38,58],"c0":[39,62,103],"c":[41],"null":[43,105],"convergent":[45],"sequences,":[46],"respectively,":[47,65],"establish":[49],"that":[50],"are":[56],"Banach":[57,101],"linearly":[59],"isomorphic":[60],"to":[61,81],"c,":[64],"obtain":[67],"their":[68],"Schauder":[69],"bases":[70],"\u03b1-,":[72],"\u03b2-":[73],"\u03b3-duals.":[75],"devote":[77],"last":[79],"section":[80],"determine":[82],"spectrum,":[84,87],"point":[86],"continuous":[89],"spectrum":[90,94],"residual":[93],"over":[99],"space":[102],"sequences.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
