{"id":"https://openalex.org/W7212476608","doi":"https://doi.org/10.48550/arxiv.2609.13116","title":"The zero set of the Zak transform of B-splines with applications to Gabor frames","display_name":"The zero set of the Zak transform of B-splines with applications to Gabor frames","publication_year":2026,"publication_date":"2026-09-11","ids":{"openalex":"https://openalex.org/W7212476608","doi":"https://doi.org/10.48550/arxiv.2609.13116"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.13116","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13116","pdf_url":"https://arxiv.org/pdf/2609.13116","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/2609.13116","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112596135","display_name":"Marzieh Hasannasab","orcid":"https://orcid.org/0000-0002-3975-5545","observed_orcids":["https://orcid.org/0000-0002-3975-5545"]},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Hasannasab, Marzieh","raw_affiliation_strings":["Technical University of Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029621633","display_name":"Jakob Lemvig","orcid":"https://orcid.org/0000-0002-9338-7755","observed_orcids":["https://orcid.org/0000-0002-9338-7755"]},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Lemvig, Jakob","raw_affiliation_strings":["Technical University of Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Denmark","institution_ids":["https://openalex.org/I96673099"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I96673099"],"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/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/zak-transform","display_name":"Zak transform","score":0.9959999918937683},{"id":"https://openalex.org/keywords/b-splines","display_name":"B-splines","score":0.9490000009536743},{"id":"https://openalex.org/keywords/zero-sets","display_name":"zero sets","score":0.7910000085830688},{"id":"https://openalex.org/keywords/gabor-frames","display_name":"Gabor frames","score":0.8259999752044678},{"id":"https://openalex.org/keywords/frame-properties","display_name":"frame properties","score":0.8619999885559082}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6435999870300293},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6172000169754028},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5286999940872192},{"id":"https://openalex.org/C173149727","wikidata":"https://www.wikidata.org/wiki/Q996397","display_name":"Gabor transform","level":4,"score":0.5267999768257141},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.5253999829292297},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4814000129699707},{"id":"https://openalex.org/C136902061","wikidata":"https://www.wikidata.org/wiki/Q16981559","display_name":"Gabor wavelet","level":5,"score":0.4453999996185303},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.37779998779296875},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36410000920295715},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.3537999987602234},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3504999876022339},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3440000116825104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.314300000667572},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2822999954223633},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28110000491142273},{"id":"https://openalex.org/C142433447","wikidata":"https://www.wikidata.org/wiki/Q7806653","display_name":"Time\u2013frequency analysis","level":3,"score":0.2797999978065491},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2752000093460083},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.27379998564720154}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.13116","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13116","pdf_url":"https://arxiv.org/pdf/2609.13116","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.2609.13116","doi":"https://doi.org/10.48550/arxiv.2609.13116","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.13116","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:2609.13116","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13116","pdf_url":"https://arxiv.org/pdf/2609.13116","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/W7212476608.pdf","grobid_xml":"https://content.openalex.org/works/W7212476608.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7206207958","https://openalex.org/W1971320783","https://openalex.org/W2145185301","https://openalex.org/W199512935","https://openalex.org/W1934956489","https://openalex.org/W4411073054","https://openalex.org/W2385029087","https://openalex.org/W2116741198","https://openalex.org/W7123643442","https://openalex.org/W2795518678"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,6,22,26,34,52,66,75],"zero":[3,23],"sets":[4],"of":[5,10,21,33,55],"Zak":[7],"transform":[8],"$Z_\u03bbB_n(x,\u03bd)$":[9],"B-splines":[11,41],"for":[12,25,29,38,69],"$\u03bb>":[13,43],"0$.":[14],"Specifically,":[15],"we":[16,46,64],"provide":[17],"a":[18],"full":[19],"characterization":[20],"set":[24],"hat":[27,76],"spline":[28],"all":[30],"positive":[31],"values":[32],"parameter":[35],"$\u03bb$":[36],"and":[37],"higher":[39],"order":[40],"when":[42],"1$.":[44],"Finally,":[45],"apply":[47],"these":[48],"results":[49],"to":[50],"establish":[51],"frame":[53,67],"property":[54,68],"integer-oversampled":[56,70],"Gabor":[57,71],"systems":[58,72],"generated":[59,73],"by":[60,74],"B-splines.":[61],"In":[62],"particular,":[63],"characterize":[65],"splines.":[77]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-15T00:00:00"}