{"id":"https://openalex.org/W7214647104","doi":"https://doi.org/10.13140/rg.2.2.19582.14402","title":"Pitt Inequalities and Logarithmic-type Uncertainty Principles for Metaplectic Operators","display_name":"Pitt Inequalities and Logarithmic-type Uncertainty Principles for Metaplectic Operators","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214647104","doi":"https://doi.org/10.13140/rg.2.2.19582.14402"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.34946","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34946","pdf_url":"https://arxiv.org/pdf/2609.34946","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.34946","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003136492","display_name":"Gianluca Giacchi","orcid":"https://orcid.org/0000-0002-6809-1311","observed_orcids":["https://orcid.org/0000-0002-6809-1311"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gianluca Giacchi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153207271","display_name":"Itamar Oliveira","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Itamar Oliveira","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5153266747","display_name":"Amy Tierney","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Amy Tierney","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":true,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9794999957084656,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9794999957084656,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.012600000016391277,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.004600000102072954,"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/metaplectic-operators","display_name":"metaplectic operators","score":0.9580000042915344},{"id":"https://openalex.org/keywords/metaplectic-group","display_name":"metaplectic group","score":0.8389999866485596},{"id":"https://openalex.org/keywords/homogeneous-sobolev-spaces","display_name":"homogeneous Sobolev spaces","score":0.9769999980926514},{"id":"https://openalex.org/keywords/quadratic-hamiltonians","display_name":"quadratic Hamiltonians","score":0.6629999876022339},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"symplectic geometry","score":0.8029999732971191}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5800999999046326},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5210000276565552},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41519999504089355},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.41119998693466187},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.35530000925064087},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.289900004863739},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27810001373291016},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.26010000705718994},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.24199999868869781}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.34946","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34946","pdf_url":"https://arxiv.org/pdf/2609.34946","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.2609.34946","doi":"https://doi.org/10.48550/arxiv.2609.34946","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.34946","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.13140/rg.2.2.19582.14402","doi":"https://doi.org/10.13140/rg.2.2.19582.14402","is_oa":false,"landing_page_url":"https://doi.org/10.13140/rg.2.2.19582.14402","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.34946","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34946","pdf_url":"https://arxiv.org/pdf/2609.34946","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G7740490836","display_name":"Multiresolution methods for unstructured data","funder_award_id":"211684","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214647104.pdf","grobid_xml":"https://content.openalex.org/works/W7214647104.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4406975472"],"related_works":["https://openalex.org/W7125686203","https://openalex.org/W4416073595","https://openalex.org/W4409413639","https://openalex.org/W4388178533","https://openalex.org/W1993240563","https://openalex.org/W4308842368","https://openalex.org/W4396708119","https://openalex.org/W7114773749","https://openalex.org/W6910543004","https://openalex.org/W4402787696"],"abstract_inverted_index":{"In":[0,139],"this":[1,39,140,163],"work,":[2],"we":[3,41,76,110],"provide":[4],"a":[5,18,74,142,155],"complete":[6],"characterisation":[7],"of":[8,57,69,85,169],"Pitt's":[9,51,78],"inequality":[10,62,79],"for":[11,80,93,117,149],"metaplectic":[12,19,71,94,119],"operators.":[13],"The":[14],"symplectic":[15],"geometry":[16,168],"underlying":[17],"operator":[20],"distinguishes":[21],"effective":[22,133],"directions,":[23,32],"along":[24,33,83],"which":[25,34],"its":[26],"action":[27],"is":[28,36],"Fourier-type,":[29],"from":[30],"singular":[31,135],"concentration":[35],"preserved.":[37],"For":[38,159],"reason,":[40],"adopt":[42],"two":[43],"complementary":[44],"perspectives,":[45],"thereby":[46],"obtaining":[47],"both":[48,131],"an":[49,60],"isotropic":[50],"inequality,":[52],"emulating":[53],"the":[54,66,70,118,124,132,150,166,170,175],"classical":[55,125],"theorem":[56],"Pitt,":[58],"and":[59,87,113,134,153,173],"anisotropic":[61],"that":[63,123],"adapts":[64],"to":[65,102],"geometric":[67],"features":[68],"group.":[72,120],"As":[73],"by-product,":[75],"obtain":[77],"Fourier":[81],"transforms":[82],"subspaces":[84],"$\\rd$":[86],"new":[88],"quantitative":[89],"time-dependent":[90,167],"boundedness":[91],"results":[92],"operators":[95],"on":[96],"homogeneous":[97],"Sobolev":[98],"spaces,":[99],"with":[100],"applications":[101],"Schr\u00f6dinger":[103,161],"evolutions":[104],"generated":[105],"by":[106],"quadratic":[107,160],"Hamiltonians.":[108],"Additionally,":[109],"derive":[111],"logarithmic":[112],"entropic":[114,126],"uncertainty":[115,127,176],"principles":[116],"We":[121],"show":[122],"principle":[128],"fails":[129],"when":[130],"directions":[136,152,172],"are":[137],"present.":[138],"case,":[141],"generally":[143],"unbounded":[144],"corrective":[145],"entropy":[146],"term":[147],"accounts":[148],"concentration-preserving":[151],"restores":[154],"meaningful":[156],"lower":[157],"bound.":[158],"evolutions,":[162],"correction":[164],"follows":[165],"nondispersive":[171],"adjusts":[174],"estimate":[177],"accordingly.":[178]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-29T00:00:00"}
