{"id":"https://openalex.org/W4403101808","doi":"https://doi.org/10.3390/sym16101307","title":"On (p,q)-Analogs of the \u03b1-th Fractional Fourier Transform and Some (p,q)-Generalized Spaces","display_name":"On (p,q)-Analogs of the \u03b1-th Fractional Fourier Transform and Some (p,q)-Generalized Spaces","publication_year":2024,"publication_date":"2024-10-03","ids":{"openalex":"https://openalex.org/W4403101808","doi":"https://doi.org/10.3390/sym16101307"},"language":"en","primary_location":{"id":"doi:10.3390/sym16101307","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16101307","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/sym16101307","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042854866","display_name":"Shrideh Al\u2010Omari","orcid":"https://orcid.org/0000-0001-8955-5552"},"institutions":[{"id":"https://openalex.org/I27570832","display_name":"Jadara University","ror":"https://ror.org/001drnv35","country_code":"JO","type":"education","lineage":["https://openalex.org/I27570832"]},{"id":"https://openalex.org/I33926330","display_name":"Al-Balqa Applied University","ror":"https://ror.org/00qedmt22","country_code":"JO","type":"education","lineage":["https://openalex.org/I33926330"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Shrideh Al-Omari","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 11134, Jordan","Jadara University Research Center, Jadara University, Irbid 21110, Jordan"],"raw_orcid":"https://orcid.org/0000-0001-8955-5552","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 11134, Jordan","institution_ids":["https://openalex.org/I33926330"]},{"raw_affiliation_string":"Jadara University Research Center, Jadara University, Irbid 21110, Jordan","institution_ids":["https://openalex.org/I27570832"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5093069500","display_name":"Wael Mahmoud Mohammad Salameh","orcid":"https://orcid.org/0009-0007-3742-6178"},"institutions":[{"id":"https://openalex.org/I117222138","display_name":"Abu Dhabi University","ror":"https://ror.org/01r3kjq03","country_code":"AE","type":"education","lineage":["https://openalex.org/I117222138"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Wael Salameh","raw_affiliation_strings":["Faculty of Information Technology, Abu Dhabi University, Abu Dhabi 59911, United Arab Emirates"],"raw_orcid":"https://orcid.org/0009-0007-3742-6178","affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, Abu Dhabi University, Abu Dhabi 59911, United Arab Emirates","institution_ids":["https://openalex.org/I117222138"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27074488,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"10","first_page":"1307","last_page":"1307"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9749000072479248,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.747357964515686},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.6146321296691895},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.6024807691574097},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5493474006652832},{"id":"https://openalex.org/keywords/generalized-function","display_name":"Generalized function","score":0.5084368586540222},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5046175718307495},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.45532655715942383},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.4110148251056671},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.333398699760437},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3230232000350952}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.747357964515686},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6146321296691895},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.6024807691574097},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5493474006652832},{"id":"https://openalex.org/C69151251","wikidata":"https://www.wikidata.org/wiki/Q846537","display_name":"Generalized function","level":2,"score":0.5084368586540222},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5046175718307495},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.45532655715942383},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.4110148251056671},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.333398699760437},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3230232000350952},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16101307","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16101307","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8446acb80b3d437aa647eff8209d8401","is_oa":false,"landing_page_url":"https://doaj.org/article/8446acb80b3d437aa647eff8209d8401","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 10, p 1307 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16101307","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16101307","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W390392975","https://openalex.org/W1984884772","https://openalex.org/W2043733517","https://openalex.org/W2052295270","https://openalex.org/W2058079568","https://openalex.org/W2059551206","https://openalex.org/W2074617333","https://openalex.org/W2090781792","https://openalex.org/W2107068648","https://openalex.org/W2109703919","https://openalex.org/W2118360351","https://openalex.org/W2141611330","https://openalex.org/W2160117308","https://openalex.org/W2316127971","https://openalex.org/W2326886507","https://openalex.org/W2400450150","https://openalex.org/W2604049126","https://openalex.org/W2794397737","https://openalex.org/W2803829382","https://openalex.org/W2963103191","https://openalex.org/W3047724700","https://openalex.org/W3082835985","https://openalex.org/W3100111522","https://openalex.org/W3129235100","https://openalex.org/W3154807851","https://openalex.org/W3164774557","https://openalex.org/W3165525681","https://openalex.org/W4240644230","https://openalex.org/W4300631328","https://openalex.org/W4366986360","https://openalex.org/W4382279236","https://openalex.org/W6721642137","https://openalex.org/W6736044509"],"related_works":["https://openalex.org/W2408620754","https://openalex.org/W2154898175","https://openalex.org/W2011368105","https://openalex.org/W3042651375","https://openalex.org/W2184985477","https://openalex.org/W1990220231","https://openalex.org/W2557365333","https://openalex.org/W4382751250","https://openalex.org/W2061233345","https://openalex.org/W4401990512"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"the":[3,6,43,56,71,81,94,97,102],"(p,q)-analogs":[4,41],"of":[5,17,23,28,42,73,83,101],"\u03b1-th":[7,44,103],"fractional":[8,45,104],"Fourier":[9,46,105],"transform":[10,47,106],"are":[11,32,48,66,107,113],"provided,":[12],"along":[13],"with":[14],"a":[15],"discussion":[16],"their":[18,110],"characteristics":[19],"in":[20,78,90],"specific":[21,64],"classes":[22],"(p,q)-generalized":[24,84],"functions.":[25],"Two":[26],"spaces":[27,57,85],"infinitely":[29],"(p,q)-differentiable":[30],"functions":[31],"defined":[33],"by":[34],"introducing":[35],"two":[36],"(p,q)-differential":[37],"symmetric":[38,75],"operators.":[39],"The":[40],"demonstrated":[49],"to":[50,63,70,92],"be":[51],"continuous":[52],"and":[53,109],"linear":[54],"between":[55],"under":[58],"discussion.":[59],"Next,":[60],"theorems":[61],"pertaining":[62],"convolutions":[65],"established.":[67],"This":[68],"leads":[69],"establishment":[72],"multiple":[74],"identities,":[76],"which":[77],"turn":[79],"requires":[80],"construction":[82],"known":[86],"as":[87],"(p,q)-Boehmians.":[88],"Finally,":[89],"addition":[91],"deriving":[93],"inversion":[95],"formulas,":[96],"generalized":[98],"(p,q)-":[99],"analogs":[100],"introduced,":[108],"general":[111],"properties":[112],"discussed.":[114]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2024-10-04T00:00:00"}
