{"id":"https://openalex.org/W7220395698","doi":"https://doi.org/10.48550/arxiv.2610.03200","title":"A Balian-Low theorem for nilpotent Lie groups","display_name":"A Balian-Low theorem for nilpotent Lie groups","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220395698","doi":"https://doi.org/10.48550/arxiv.2610.03200"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03200","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03200","pdf_url":"https://arxiv.org/pdf/2610.03200","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":"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/2610.03200","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054871643","display_name":"Ulrik Enstad","orcid":"https://orcid.org/0000-0001-7601-4140","observed_orcids":["https://orcid.org/0000-0001-7601-4140"]},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Enstad, Ulrik","raw_affiliation_strings":["Faculty of Mathematics , University of Vienna , Oskar-Morgenstern-Platz 1 , 1090 Vienna , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics , University of Vienna , Oskar-Morgenstern-Platz 1 , 1090 Vienna , Austria","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057083663","display_name":"Jordy Timo van Velthoven","orcid":"https://orcid.org/0000-0002-8529-4516","observed_orcids":["https://orcid.org/0000-0002-8529-4516"]},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"van Velthoven, Jordy Timo","raw_affiliation_strings":["Faculty of Mathematics , University of Vienna , Oskar-Morgenstern-Platz 1 , 1090 Vienna , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics , University of Vienna , Oskar-Morgenstern-Platz 1 , 1090 Vienna , Austria","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I129774422"],"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":1.0,"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":1.0,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/balian-low-theorem","display_name":"Balian-Low theorem","score":0.9909999966621399},{"id":"https://openalex.org/keywords/nilpotent-lie-groups","display_name":"nilpotent Lie groups","score":0.9950000047683716},{"id":"https://openalex.org/keywords/riesz-sequences","display_name":"Riesz sequences","score":0.9980000257492065},{"id":"https://openalex.org/keywords/homogeneous-groups","display_name":"homogeneous groups","score":0.6430000066757202},{"id":"https://openalex.org/keywords/representation-stability","display_name":"representation stability","score":0.6690000295639038},{"id":"https://openalex.org/keywords/gabor-frames","display_name":"Gabor frames","score":0.5899999737739563},{"id":"https://openalex.org/keywords/time-frequency-analysis","display_name":"time-frequency analysis","score":0.5809999704360962}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8822000026702881},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.7972000241279602},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.7445999979972839},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6434999704360962},{"id":"https://openalex.org/C206219070","wikidata":"https://www.wikidata.org/wiki/Q1755242","display_name":"Nilpotent group","level":3,"score":0.5634999871253967},{"id":"https://openalex.org/C22365015","wikidata":"https://www.wikidata.org/wiki/Q1003162","display_name":"Simple Lie group","level":3,"score":0.5541999936103821},{"id":"https://openalex.org/C58910974","wikidata":"https://www.wikidata.org/wiki/Q1017106","display_name":"Adjoint representation","level":3,"score":0.4984999895095825},{"id":"https://openalex.org/C27563320","wikidata":"https://www.wikidata.org/wiki/Q650670","display_name":"Nilpotent matrix","level":5,"score":0.48660001158714294},{"id":"https://openalex.org/C186489112","wikidata":"https://www.wikidata.org/wiki/Q763735","display_name":"Representation of a Lie group","level":3,"score":0.48010000586509705},{"id":"https://openalex.org/C130133044","wikidata":"https://www.wikidata.org/wiki/Q1887083","display_name":"Compact group","level":3,"score":0.46639999747276306},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.44440001249313354},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.40529999136924744},{"id":"https://openalex.org/C205633959","wikidata":"https://www.wikidata.org/wiki/Q2494915","display_name":"Unipotent","level":2,"score":0.3950999975204468},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.38659998774528503},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.3677000105381012},{"id":"https://openalex.org/C188440111","wikidata":"https://www.wikidata.org/wiki/Q5062152","display_name":"Central series","level":4,"score":0.3643999993801117},{"id":"https://openalex.org/C2776456406","wikidata":"https://www.wikidata.org/wiki/Q6664692","display_name":"Locally nilpotent","level":4,"score":0.3634999990463257},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.35199999809265137},{"id":"https://openalex.org/C5106717","wikidata":"https://www.wikidata.org/wiki/Q3427416","display_name":"Fundamental representation","level":4,"score":0.3352000117301941},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3334999978542328},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3244999945163727},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.32170000672340393},{"id":"https://openalex.org/C143135876","wikidata":"https://www.wikidata.org/wiki/Q357300","display_name":"Lie theory","level":5,"score":0.3147999942302704},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.310699999332428},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3037000000476837},{"id":"https://openalex.org/C197893656","wikidata":"https://www.wikidata.org/wiki/Q1000120","display_name":"Maximal torus","level":5,"score":0.2994999885559082},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2849000096321106},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C2776122010","wikidata":"https://www.wikidata.org/wiki/Q10359539","display_name":"Unitary representation","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.25209999084472656},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.25200000405311584},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03200","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03200","pdf_url":"https://arxiv.org/pdf/2610.03200","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.03200","doi":"https://doi.org/10.48550/arxiv.2610.03200","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03200","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.03200","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03200","pdf_url":"https://arxiv.org/pdf/2610.03200","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G9000045241","display_name":null,"funder_award_id":"10.55776/PAT2545623","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G935911571","display_name":"Coherent states and multiparameter singular integrals","funder_award_id":"PAT 2545623","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220395698.pdf","grobid_xml":"https://content.openalex.org/works/W7220395698.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2800349537","https://openalex.org/W4415089172","https://openalex.org/W7213878816"],"related_works":["https://openalex.org/W4288264857","https://openalex.org/W3186906123","https://openalex.org/W4281567680","https://openalex.org/W2804168212","https://openalex.org/W7148357569","https://openalex.org/W4415248058","https://openalex.org/W4405400551","https://openalex.org/W2032895776","https://openalex.org/W2091413486","https://openalex.org/W4386091417"],"abstract_inverted_index":{"We":[0],"prove":[1,45],"strict":[2],"necessary":[3],"density":[4],"conditions":[5],"for":[6,28,49],"smooth":[7],"coherent":[8,50],"frames":[9,51],"and":[10,52],"Riesz":[11,53],"sequences":[12,54],"in":[13,39],"the":[14],"orbit":[15],"of":[16],"a":[17,46],"connected,":[18,20],"simply":[19],"nilpotent":[21,33],"Lie":[22,34],"group.":[23],"This":[24],"extends":[25],"previous":[26],"results":[27],"homogeneous":[29],"groups":[30],"to":[31],"general":[32],"groups.":[35],"The":[36],"main":[37],"novelty":[38],"our":[40],"approach":[41],"is":[42],"that":[43],"we":[44],"stability":[47],"result":[48],"based":[55],"on":[56],"deforming":[57],"their":[58,62],"representation":[59],"rather":[60],"than":[61],"index":[63],"set.":[64]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}