{"id":"https://openalex.org/W4404717841","doi":"https://doi.org/10.1007/s11118-024-10174-0","title":"The Liouville Theorem for Discrete Symmetric Averaging Operators","display_name":"The Liouville Theorem for Discrete Symmetric Averaging Operators","publication_year":2024,"publication_date":"2024-11-26","ids":{"openalex":"https://openalex.org/W4404717841","doi":"https://doi.org/10.1007/s11118-024-10174-0"},"language":"en","primary_location":{"id":"doi:10.1007/s11118-024-10174-0","doi":"https://doi.org/10.1007/s11118-024-10174-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11118-024-10174-0","pdf_url":null,"source":{"id":"https://openalex.org/S71596206","display_name":"Potential Analysis","issn_l":"0926-2601","issn":["0926-2601","1572-929X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Potential Analysis","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s11118-024-10174-0","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057151946","display_name":"Tomasz Adamowicz","orcid":"https://orcid.org/0000-0003-1215-2784","observed_orcids":["https://orcid.org/0000-0003-1215-2784"]},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Tomasz Adamowicz","raw_affiliation_strings":["Institute of Mathematics, Polish Academy of Sciences, \u015aniadeckich 8, Warsaw, 00-656, Poland"],"raw_orcid":"https://orcid.org/0000-0003-1215-2784","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Polish Academy of Sciences, \u015aniadeckich 8, Warsaw, 00-656, Poland","institution_ids":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048033147","display_name":"Jos\u00e9 G. Llorente","orcid":"https://orcid.org/0000-0002-6952-0640","observed_orcids":["https://orcid.org/0000-0002-6952-0640"]},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 G. Llorente","raw_affiliation_strings":["Departamento de An\u00e1lisis Matem\u00e1tico y Matem\u00e1tica Aplicada and Instituto de Matem\u00e1tica Interdisciplinar (IMI), Facultad de Matem\u00e1ticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid, 28040, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de An\u00e1lisis Matem\u00e1tico y Matem\u00e1tica Aplicada and Instituto de Matem\u00e1tica Interdisciplinar (IMI), Facultad de Matem\u00e1ticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid, 28040, Spain","institution_ids":["https://openalex.org/I121748325"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057151946"],"corresponding_institution_ids":["https://openalex.org/I4210137370","https://openalex.org/I99542240"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27375118,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"63","issue":"1","first_page":"431","last_page":"446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.6220999956130981,"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"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.6220999956130981,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.3292999863624573,"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/T13234","display_name":"advanced mathematical theories","score":0.02410000003874302,"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/liouville-s-theorem","display_name":"Liouville's theorem","score":0.9789999723434448},{"id":"https://openalex.org/keywords/mean-value-property","display_name":"mean value property","score":0.6959999799728394},{"id":"https://openalex.org/keywords/discrete-harmonic-functions","display_name":"discrete harmonic functions","score":0.9110000133514404},{"id":"https://openalex.org/keywords/p-harmonic-functions","display_name":"p-harmonic functions","score":0.9929999709129333},{"id":"https://openalex.org/keywords/infinity-harmonic-functions","display_name":"infinity harmonic functions","score":0.9150000214576721},{"id":"https://openalex.org/keywords/lattice-z-d","display_name":"lattice Z^d","score":0.6600000262260437},{"id":"https://openalex.org/keywords/discrete-potential-theory","display_name":"discrete potential theory","score":0.5830000042915344}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49741223454475403},{"id":"https://openalex.org/C627467","wikidata":"https://www.wikidata.org/wiki/Q599027","display_name":"Harmonic function","level":2,"score":0.49145495891571045},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44233277440071106},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4276011884212494},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2620357275009155},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1956518590450287},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06806418299674988}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11118-024-10174-0","doi":"https://doi.org/10.1007/s11118-024-10174-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11118-024-10174-0","pdf_url":null,"source":{"id":"https://openalex.org/S71596206","display_name":"Potential Analysis","issn_l":"0926-2601","issn":["0926-2601","1572-929X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Potential Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2204.12295","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2204.12295","pdf_url":"https://arxiv.org/pdf/2204.12295","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2204.12295","doi":"https://doi.org/10.48550/arxiv.2204.12295","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2204.12295","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,"listed_in":[],"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:10.1007/s11118-024-10174-0","doi":"https://doi.org/10.1007/s11118-024-10174-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11118-024-10174-0","pdf_url":null,"source":{"id":"https://openalex.org/S71596206","display_name":"Potential Analysis","issn_l":"0926-2601","issn":["0926-2601","1572-929X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Potential Analysis","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1100101037","display_name":null,"funder_award_id":"346300","funder_id":"https://openalex.org/F4320322733","funder_display_name":"Ministerstwo Edukacji i Nauki"},{"id":"https://openalex.org/G1267233363","display_name":null,"funder_award_id":"MTM2017- 85666-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G2346625195","display_name":null,"funder_award_id":"2015\u20132019","funder_id":"https://openalex.org/F4320322733","funder_display_name":"Ministerstwo Edukacji i Nauki"},{"id":"https://openalex.org/G3320837874","display_name":null,"funder_award_id":"346300","funder_id":"https://openalex.org/F4320336152","funder_display_name":"Instytut Matematyczny, Polskiej Akademii Nauk"},{"id":"https://openalex.org/G7473301749","display_name":null,"funder_award_id":"2015-2019","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G869270362","display_name":null,"funder_award_id":"UMO-2017/25/B/ST1/01955","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"}],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320322511","display_name":"Narodowe Centrum Nauki","ror":"https://ror.org/03ha2q922"},{"id":"https://openalex.org/F4320322733","display_name":"Ministerstwo Edukacji i Nauki","ror":"https://ror.org/05dwvd537"},{"id":"https://openalex.org/F4320336152","display_name":"Instytut Matematyczny, Polskiej Akademii Nauk","ror":"https://ror.org/04hrrh248"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1826824261","https://openalex.org/W1964041556","https://openalex.org/W1984072091","https://openalex.org/W1987642543","https://openalex.org/W2007676601","https://openalex.org/W2010968963","https://openalex.org/W2055207932","https://openalex.org/W2066590618","https://openalex.org/W2080585029","https://openalex.org/W2129277185","https://openalex.org/W2131861355","https://openalex.org/W2339026534","https://openalex.org/W2508062351","https://openalex.org/W2566493574","https://openalex.org/W2617595374","https://openalex.org/W2890653944","https://openalex.org/W2913904020","https://openalex.org/W2962826709","https://openalex.org/W2963153497","https://openalex.org/W3098296886","https://openalex.org/W3175712172","https://openalex.org/W3184227926","https://openalex.org/W4226333864","https://openalex.org/W4237766876","https://openalex.org/W4246047487"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W2360188928","https://openalex.org/W2887720363","https://openalex.org/W4236509407","https://openalex.org/W3193633018","https://openalex.org/W4221155962"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"introduce":[2],"averaging":[3],"operators":[4],"on":[5,57],"lattices":[6],"$$\\mathbb":[7,58],"Z^d$$":[8,59],"Z":[9,60],"d":[10,61],"and":[11,36],"study":[12],"the":[13,37,50],"Liouville":[14,51],"property":[15],"for":[16,53],"functions":[17,56],"satisfying":[18],"mean":[19],"value":[20],"properties":[21],"associated":[22],"to":[23],"such":[24],"operators.":[25],"This":[26],"framework":[27],"encloses":[28],"discrete":[29],"harmonic,":[30],"p-harmonic,":[31],"$$\\infty":[32],"$$":[33],"\u221e":[34],"-harmonic":[35],"so-called":[38],"game":[39],"p-harmonic":[40,55],"functions.":[41],"Our":[42],"approach":[43],"provides":[44],"an":[45],"elementary":[46],"alternative":[47],"proof":[48],"of":[49],"Theorem":[52],"positive":[54],".":[62]},"counts_by_year":[],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}
