{"id":"https://openalex.org/W7224928116","doi":"https://doi.org/10.48550/arxiv.2610.40508","title":"Differentiation and Shift Property Characterisations of the Group Fourier Transform on the Heisenberg Group","display_name":"Differentiation and Shift Property Characterisations of the Group Fourier Transform on the Heisenberg Group","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224928116","doi":"https://doi.org/10.48550/arxiv.2610.40508"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.40508","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.40508","pdf_url":"https://arxiv.org/pdf/2610.40508","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.40508","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101709448","display_name":"R\u200e. \u200eLakshmi Lavanya","orcid":"https://orcid.org/0000-0002-2423-8684","observed_orcids":["https://orcid.org/0000-0002-2423-8684"]},"institutions":[{"id":"https://openalex.org/I4210140410","display_name":"Indian Institute of Science Education and Research, Tirupati","ror":"https://ror.org/032d0e990","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210140410"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Lavanya, R. Lakshmi","raw_affiliation_strings":["Department of Mathematics , Indian Institute of Science Education and Research (IISER) Tirupati , Tirupati -517 619 "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Indian Institute of Science Education and Research (IISER) Tirupati , Tirupati -517 619 ","institution_ids":["https://openalex.org/I4210140410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101709448"],"corresponding_institution_ids":["https://openalex.org/I4210140410"],"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":0.9878000020980835,"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":0.9878000020980835,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.007600000128149986,"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":0.0017000000225380063,"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/fourier-transform-on-groups","display_name":"group Fourier transform","score":0.9300000071525574},{"id":"https://openalex.org/keywords/heisenberg-group","display_name":"Heisenberg group","score":1.0},{"id":"https://openalex.org/keywords/left-invariant-vector-fields","display_name":"left-invariant vector fields","score":0.8299999833106995},{"id":"https://openalex.org/keywords/right-translations","display_name":"right translations","score":0.996999979019165},{"id":"https://openalex.org/keywords/locally-compact-abelian-groups","display_name":"locally compact abelian groups","score":0.8669999837875366},{"id":"https://openalex.org/keywords/integral-transforms","display_name":"integral transforms","score":0.6320000290870667}],"concepts":[{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.7616999745368958},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7141000032424927},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6283000111579895},{"id":"https://openalex.org/C127519595","wikidata":"https://www.wikidata.org/wiki/Q1601337","display_name":"Heisenberg group","level":2,"score":0.5859000086784363},{"id":"https://openalex.org/C67757890","wikidata":"https://www.wikidata.org/wiki/Q1567607","display_name":"Hartley transform","level":5,"score":0.5450000166893005},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49160000681877136},{"id":"https://openalex.org/C175146775","wikidata":"https://www.wikidata.org/wiki/Q3984053","display_name":"Fourier inversion theorem","level":5,"score":0.46470001339912415},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.4584999978542328},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.43140000104904175},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4108999967575073},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4088999927043915},{"id":"https://openalex.org/C50826107","wikidata":"https://www.wikidata.org/wiki/Q5475803","display_name":"Fourier transform on finite groups","level":5,"score":0.40849998593330383},{"id":"https://openalex.org/C99234102","wikidata":"https://www.wikidata.org/wiki/Q7395403","display_name":"S transform","level":5,"score":0.39739999175071716},{"id":"https://openalex.org/C200052193","wikidata":"https://www.wikidata.org/wiki/Q877802","display_name":"Integral transform","level":2,"score":0.3765999972820282},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C130133044","wikidata":"https://www.wikidata.org/wiki/Q1887083","display_name":"Compact group","level":3,"score":0.3630000054836273},{"id":"https://openalex.org/C166386157","wikidata":"https://www.wikidata.org/wiki/Q1477735","display_name":"Short-time Fourier transform","level":4,"score":0.36160001158714294},{"id":"https://openalex.org/C47615080","wikidata":"https://www.wikidata.org/wiki/Q1328722","display_name":"Sine and cosine transforms","level":5,"score":0.33899998664855957},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C181543814","wikidata":"https://www.wikidata.org/wiki/Q44746","display_name":"Uncertainty principle","level":3,"score":0.3352999985218048},{"id":"https://openalex.org/C1109138","wikidata":"https://www.wikidata.org/wiki/Q3280930","display_name":"Harmonic wavelet transform","level":5,"score":0.335099995136261},{"id":"https://openalex.org/C10288518","wikidata":"https://www.wikidata.org/wiki/Q1785576","display_name":"Two-sided Laplace transform","level":5,"score":0.3059999942779541},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C95722684","wikidata":"https://www.wikidata.org/wiki/Q2622756","display_name":"Continuous wavelet transform","level":5,"score":0.29919999837875366},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.28459998965263367},{"id":"https://openalex.org/C199874217","wikidata":"https://www.wikidata.org/wiki/Q606934","display_name":"Mellin transform","level":3,"score":0.2840999960899353},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C62058723","wikidata":"https://www.wikidata.org/wiki/Q7049066","display_name":"Non-uniform discrete Fourier transform","level":5,"score":0.2619999945163727},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.2578999996185303},{"id":"https://openalex.org/C122444316","wikidata":"https://www.wikidata.org/wiki/Q1440048","display_name":"Discrete-time Fourier transform","level":5,"score":0.2556000053882599},{"id":"https://openalex.org/C158650840","wikidata":"https://www.wikidata.org/wiki/Q907439","display_name":"Dirac operator","level":2,"score":0.2529999911785126}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.40508","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.40508","pdf_url":"https://arxiv.org/pdf/2610.40508","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.2610.40508","doi":"https://doi.org/10.48550/arxiv.2610.40508","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.40508","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.40508","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.40508","pdf_url":"https://arxiv.org/pdf/2610.40508","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224928116.pdf","grobid_xml":"https://content.openalex.org/works/W7224928116.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7099482799","https://openalex.org/W2008411408","https://openalex.org/W2381582447","https://openalex.org/W4400380194","https://openalex.org/W920731669","https://openalex.org/W2033385045","https://openalex.org/W1987400337","https://openalex.org/W4362700264","https://openalex.org/W58101874","https://openalex.org/W3159909844"],"abstract_inverted_index":{"Recently,":[0],"Krukowski":[1],"characterised":[2],"the":[3,8,31,34,38,46,71,83,88,92,100,103,110,115,130,135,149],"classical":[4],"Fourier":[5,35,85,105,132],"transform":[6,36,54,86,106,133,150,164],"on":[7,30,87,120,134],"real":[9],"line":[10],"in":[11,97],"terms":[12,98],"of":[13,33,41,99,102,127],"its":[14,121],"behaviour":[15,32,101,122],"with":[16,63,107,140],"respect":[17,108],"to":[18,69,109,160],"differentiation.":[19],"For":[20],"locally":[21],"compact":[22],"abelian":[23],"groups,":[24],"he":[25,67],"obtained":[26],"a":[27,56,64,141,165],"characterisation":[28],"based":[29,119],"under":[37,123],"shift.":[39],"Each":[40],"these":[42,128],"results":[43,81,146],"assumed":[44],"that":[45,148],"operator":[47],"(to":[48],"be":[49,161],"characterised)":[50],"is":[51,95,118,151],"an":[52,162],"integral":[53,163],"(with":[55],"kernel":[57],"satisfying":[58],"suitable":[59],"regularity":[60],"conditions),":[61],"paired":[62,139],"normalisation":[65],"which":[66],"refers":[68],"as":[70],"Dirac":[72,142],"delta":[73,143],"property.":[74,144],"In":[75],"this":[76],"paper,":[77],"we":[78],"obtain":[79],"analogous":[80],"for":[82],"group":[84,104,131],"Heisenberg":[89,136],"group.":[90],"Here,":[91],"differentiation":[93],"property":[94,117],"formulated":[96],"left-invariant":[111],"vector":[112],"fields,":[113],"and":[114,153,155],"shift":[116],"right":[124],"translation.":[125],"Both":[126],"characterise":[129],"group,":[137],"once":[138],"Our":[145],"assume":[147],"continuous":[152],"linear,":[154],"do":[156],"not":[157],"require":[158],"it":[159],"priori.":[166]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-10-31T00:00:00"}