{"id":"https://openalex.org/W7204844705","doi":"https://doi.org/10.1080/10652469.2026.2723983","title":"Hankel, fractional Hankel, and Bessel wavelet transforms of almost periodic signals: product-type and spherical extensions in n variables","display_name":"Hankel, fractional Hankel, and Bessel wavelet transforms of almost periodic signals: product-type and spherical extensions in n variables","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204844705","doi":"https://doi.org/10.1080/10652469.2026.2723983"},"language":"en","primary_location":{"id":"doi:10.1080/10652469.2026.2723983","doi":"https://doi.org/10.1080/10652469.2026.2723983","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10652469.2026.2723983","pdf_url":null,"source":{"id":"https://openalex.org/S77852275","display_name":"Integral Transforms and Special Functions","issn_l":"1065-2469","issn":["1065-2469","1476-8291"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Integral Transforms and Special Functions","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075717348","display_name":"Balasaheb Bhagaji Waphare","orcid":"https://orcid.org/0000-0003-0976-0615","observed_orcids":["https://orcid.org/0000-0003-0976-0615"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Balasaheb B. Waphare","raw_affiliation_strings":["MIT Arts, Commerce and Science College (MITACSC)"],"raw_orcid":"https://orcid.org/0000-0003-0976-0615","affiliations":[{"raw_affiliation_string":"MIT Arts, Commerce and Science College (MITACSC)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5075717348"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"16"},"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/T11049","display_name":"Advanced Harmonic Analysis Research","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"}},{"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/hankel-transform","display_name":"Hankel transform","score":0.9520000219345093},{"id":"https://openalex.org/keywords/spherical-wavelet-transform","display_name":"spherical wavelet transform","score":0.574999988079071},{"id":"https://openalex.org/keywords/boundedness-estimates","display_name":"boundedness estimates","score":0.8679999709129333}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8815000057220459},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.8019999861717224},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6492999792098999},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5813999772071838},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5324000120162964},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.5127999782562256},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4668999910354614},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4487999975681305},{"id":"https://openalex.org/C118532472","wikidata":"https://www.wikidata.org/wiki/Q4896405","display_name":"Bessel process","level":5,"score":0.4075999855995178},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37439998984336853},{"id":"https://openalex.org/C162355945","wikidata":"https://www.wikidata.org/wiki/Q1066983","display_name":"Almost periodic function","level":2,"score":0.37400001287460327},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.32440000772476196},{"id":"https://openalex.org/C181543814","wikidata":"https://www.wikidata.org/wiki/Q44746","display_name":"Uncertainty principle","level":3,"score":0.299699991941452},{"id":"https://openalex.org/C137665795","wikidata":"https://www.wikidata.org/wiki/Q7576710","display_name":"Spherical mean","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2743000090122223},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.26919999718666077},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.26159998774528503},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.25940001010894775},{"id":"https://openalex.org/C168460219","wikidata":"https://www.wikidata.org/wiki/Q1502167","display_name":"Iterated function system","level":3,"score":0.25859999656677246}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10652469.2026.2723983","doi":"https://doi.org/10.1080/10652469.2026.2723983","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10652469.2026.2723983","pdf_url":null,"source":{"id":"https://openalex.org/S77852275","display_name":"Integral Transforms and Special Functions","issn_l":"1065-2469","issn":["1065-2469","1476-8291"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Integral Transforms and Special Functions","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1800418436","https://openalex.org/W2003101564","https://openalex.org/W2011451092","https://openalex.org/W2027385203","https://openalex.org/W2035344387","https://openalex.org/W2129864213","https://openalex.org/W2145576488","https://openalex.org/W2195777306","https://openalex.org/W4231032526","https://openalex.org/W4254854117","https://openalex.org/W4292399988"],"related_works":["https://openalex.org/W2195777306","https://openalex.org/W2749920012","https://openalex.org/W2805445481","https://openalex.org/W4362635136","https://openalex.org/W2602865715","https://openalex.org/W4293761123","https://openalex.org/W1570517554","https://openalex.org/W3194708419","https://openalex.org/W3145449444","https://openalex.org/W2778263342"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,30,51,110,121],"theory":[3,36],"of":[4,93,113,139],"n-variable":[5],"Hankel,":[6,8],"fractional":[7],"and":[9,45,49,68,98,102,126],"Bessel":[10,59],"wavelet":[11],"transforms":[12],"for":[13],"almost":[14,85],"periodic":[15,86],"signals,":[16],"where":[17],"n\u22652":[18],"is":[19],"an":[20,127,130],"arbitrary":[21],"positive":[22],"integer.":[23],"Two":[24],"complementary":[25],"approaches":[26],"are":[27,88],"pursued:":[28],"(i)":[29],"product-type":[31],"construction":[32,54],"extending":[33],"the":[34,56,91,114,136,140,149,154],"one-variable":[35],"coordinate-by-coordinate,":[37],"with":[38,117],"complete":[39],"proofs":[40],"including":[41],"detailed":[42],"cross-term":[43],"estimates":[44,101],"explicit":[46],"density":[47],"arguments;":[48],"(ii)":[50],"windowed":[52],"spherical":[53,58,124],"using":[55],"n-dimensional":[57,131],"kernel,":[60],"which":[61],"genuinely":[62,122],"couples":[63],"all":[64],"n":[65],"spatial":[66],"variables":[67],"cannot":[69],"be":[70],"reduced":[71],"to":[72,129],"iterated":[73],"one-dimensional":[74],"transforms.":[75],"For":[76],"each":[77],"construction,":[78],"we":[79],"establish":[80],"Parseval-type":[81],"identities,":[82],"prove":[83],"that":[84],"functions":[87],"mapped":[89],"into":[90],"space":[92],"strong":[94],"limit":[95],"power":[96],"functions,":[97],"derive":[99],"boundedness":[100,115],"generalized":[103],"frame":[104],"decompositions.":[105],"Three":[106],"worked":[107],"examples,":[108],"namely":[109],"numerical":[111],"verification":[112],"estimate":[116],"explicitly":[118],"computed":[119],"constants,":[120],"non-separable":[123],"example,":[125],"application":[128],"Bessel-type":[132],"diffusion":[133],"equation,":[134],"validate":[135],"practical":[137],"utility":[138],"results.":[141],"The":[142],"three-variable":[143],"case":[144],"(n":[145],"=":[146],"3)":[147],"recovers":[148],"results":[150],"previously":[151],"established":[152],"by":[153],"author.":[155]},"counts_by_year":[],"updated_date":"2026-09-23T05:00:35.095934","created_date":"2026-09-01T00:00:00"}
