{"id":"https://openalex.org/W4388494173","doi":"https://doi.org/10.1137/23m1560628","title":"The Fourier, Hilbert, and Mellin Transforms on a Half-Line","display_name":"The Fourier, Hilbert, and Mellin Transforms on a Half-Line","publication_year":2023,"publication_date":"2023-11-08","ids":{"openalex":"https://openalex.org/W4388494173","doi":"https://doi.org/10.1137/23m1560628"},"language":"en","primary_location":{"id":"doi:10.1137/23m1560628","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/23m1560628","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lutpub.lut.fi/bitstream/10024/166824/1/bl%c3%a5sten_et_al_the_fourier_aam.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023018271","display_name":"Emilia Bl\u00e5sten","orcid":"https://orcid.org/0000-0001-6675-6108"},"institutions":[{"id":"https://openalex.org/I111112146","display_name":"Tallinn University of Technology","ror":"https://ror.org/0443cwa12","country_code":"EE","type":"education","lineage":["https://openalex.org/I111112146"]},{"id":"https://openalex.org/I63548447","display_name":"Lappeenranta-Lahti University of Technology","ror":"https://ror.org/0208vgz68","country_code":"FI","type":"education","lineage":["https://openalex.org/I63548447"]}],"countries":["EE","FI"],"is_corresponding":true,"raw_author_name":"Emilia L. K. Bl\u00e5sten","raw_affiliation_strings":["Computational Engineering, School of Engineering Science, LUT University, 15210 Lahti, Finland","Division of Mathematics, Tallinn University of Technology, Department of Cybernetics, 19086 Tallinn, Estonia"],"affiliations":[{"raw_affiliation_string":"Computational Engineering, School of Engineering Science, LUT University, 15210 Lahti, Finland","institution_ids":["https://openalex.org/I63548447"]},{"raw_affiliation_string":"Division of Mathematics, Tallinn University of Technology, Department of Cybernetics, 19086 Tallinn, Estonia","institution_ids":["https://openalex.org/I111112146"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088315215","display_name":"Lassi Pa\u00efv\u00e4rinta","orcid":null},"institutions":[{"id":"https://openalex.org/I111112146","display_name":"Tallinn University of Technology","ror":"https://ror.org/0443cwa12","country_code":"EE","type":"education","lineage":["https://openalex.org/I111112146"]}],"countries":["EE"],"is_corresponding":false,"raw_author_name":"Lassi P\u00e4iv\u00e4rinta","raw_affiliation_strings":["Division of Mathematics, Tallinn University of Technology, Department of Cybernetics, 19086 Tallinn, Estonia"],"affiliations":[{"raw_affiliation_string":"Division of Mathematics, Tallinn University of Technology, Department of Cybernetics, 19086 Tallinn, Estonia","institution_ids":["https://openalex.org/I111112146"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090459468","display_name":"Sadia Sadique","orcid":"https://orcid.org/0000-0002-4957-0616"},"institutions":[{"id":"https://openalex.org/I111112146","display_name":"Tallinn University of Technology","ror":"https://ror.org/0443cwa12","country_code":"EE","type":"education","lineage":["https://openalex.org/I111112146"]}],"countries":["EE"],"is_corresponding":false,"raw_author_name":"Sadia Sadique","raw_affiliation_strings":["Division of Mathematics, Tallinn University of Technology, Department of Cybernetics, 19086 Tallinn, Estonia"],"affiliations":[{"raw_affiliation_string":"Division of Mathematics, Tallinn University of Technology, Department of Cybernetics, 19086 Tallinn, Estonia","institution_ids":["https://openalex.org/I111112146"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023018271"],"corresponding_institution_ids":["https://openalex.org/I111112146","https://openalex.org/I63548447"],"apc_list":null,"apc_paid":null,"fwci":0.5412,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.61495078,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"55","issue":"6","first_page":"7529","last_page":"7548"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998000264167786,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mellin-transform","display_name":"Mellin transform","score":0.8799128532409668},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7279913425445557},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.6525599956512451},{"id":"https://openalex.org/keywords/hilbert-transform","display_name":"Hilbert transform","score":0.6359772086143494},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.6103132963180542},{"id":"https://openalex.org/keywords/mellin-inversion-theorem","display_name":"Mellin inversion theorem","score":0.6050724983215332},{"id":"https://openalex.org/keywords/two-sided-laplace-transform","display_name":"Two-sided Laplace transform","score":0.5931276679039001},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.5554971694946289},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5426216125488281},{"id":"https://openalex.org/keywords/hartley-transform","display_name":"Hartley transform","score":0.47513821721076965},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.465999960899353},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.46082603931427},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4373665452003479},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43082094192504883},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.21644598245620728}],"concepts":[{"id":"https://openalex.org/C199874217","wikidata":"https://www.wikidata.org/wiki/Q606934","display_name":"Mellin transform","level":3,"score":0.8799128532409668},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7279913425445557},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6525599956512451},{"id":"https://openalex.org/C28799612","wikidata":"https://www.wikidata.org/wiki/Q685437","display_name":"Hilbert transform","level":3,"score":0.6359772086143494},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6103132963180542},{"id":"https://openalex.org/C179766858","wikidata":"https://www.wikidata.org/wiki/Q6813106","display_name":"Mellin inversion theorem","level":5,"score":0.6050724983215332},{"id":"https://openalex.org/C10288518","wikidata":"https://www.wikidata.org/wiki/Q1785576","display_name":"Two-sided Laplace transform","level":5,"score":0.5931276679039001},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5554971694946289},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5426216125488281},{"id":"https://openalex.org/C67757890","wikidata":"https://www.wikidata.org/wiki/Q1567607","display_name":"Hartley transform","level":5,"score":0.47513821721076965},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.465999960899353},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.46082603931427},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4373665452003479},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43082094192504883},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.21644598245620728},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/23m1560628","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/23m1560628","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:lutpub.lut.fi:10024/166824","is_oa":true,"landing_page_url":"https://lutpub.lut.fi/handle/10024/166824","pdf_url":"https://lutpub.lut.fi/bitstream/10024/166824/1/bl%c3%a5sten_et_al_the_fourier_aam.pdf","source":{"id":"https://openalex.org/S4306402474","display_name":"LUTPub (LUT University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63548447","host_organization_name":"Lappeenranta-Lahti University of Technology","host_organization_lineage":["https://openalex.org/I63548447"],"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":"","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:lutpub.lut.fi:10024/166824","is_oa":true,"landing_page_url":"https://lutpub.lut.fi/handle/10024/166824","pdf_url":"https://lutpub.lut.fi/bitstream/10024/166824/1/bl%c3%a5sten_et_al_the_fourier_aam.pdf","source":{"id":"https://openalex.org/S4306402474","display_name":"LUTPub (LUT University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63548447","host_organization_name":"Lappeenranta-Lahti University of Technology","host_organization_lineage":["https://openalex.org/I63548447"],"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":"","raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.5}],"awards":[{"id":"https://openalex.org/G12851767","display_name":"Centre of Excellence of Inverse Modelling and Imaging","funder_award_id":"336787","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"},{"id":"https://openalex.org/G2997325650","display_name":null,"funder_award_id":"336787","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"},{"id":"https://openalex.org/G4031803970","display_name":null,"funder_award_id":"PRG 832","funder_id":"https://openalex.org/F4320321090","funder_display_name":"Eesti Teadusagentuur"},{"id":"https://openalex.org/G7401428671","display_name":null,"funder_award_id":"312124","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"}],"funders":[{"id":"https://openalex.org/F4320321090","display_name":"Eesti Teadusagentuur","ror":"https://ror.org/00jjeja18"},{"id":"https://openalex.org/F4320321108","display_name":"Academy of Finland","ror":"https://ror.org/05k73zm37"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4388494173.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W601470271","https://openalex.org/W1965698827","https://openalex.org/W1996588645","https://openalex.org/W2000278290","https://openalex.org/W2002357257","https://openalex.org/W2021301220","https://openalex.org/W2062202343","https://openalex.org/W2086237130","https://openalex.org/W2325538405","https://openalex.org/W2498026024","https://openalex.org/W2501012592","https://openalex.org/W2600828523","https://openalex.org/W3043440853","https://openalex.org/W3146073576","https://openalex.org/W4240555338","https://openalex.org/W4241668380","https://openalex.org/W4249274673","https://openalex.org/W4249385895"],"related_works":["https://openalex.org/W2786944155","https://openalex.org/W2783044681","https://openalex.org/W1519876566","https://openalex.org/W2076620254","https://openalex.org/W2066248978","https://openalex.org/W2341216038","https://openalex.org/W2120173888","https://openalex.org/W2485378330","https://openalex.org/W2358495801","https://openalex.org/W2097235826"],"abstract_inverted_index":{"We":[0,53],"are":[1],"interested":[2],"in":[3,49,98],"the":[4,8,13,20,38,60,65,86,89,99,102,107,111,118],"singular":[5],"behavior":[6],"at":[7],"origin":[9],"of":[10,59,117],"solutions":[11],"to":[12,40,83],"equation":[14],"on":[15,37,110],"a":[16,28,33,50,57,122],"half-axis,":[17],"where":[18,63],"is":[19,32,64,105],"one-sided":[21],"Hilbert":[22,92],"transform,":[23],"an":[24],"unknown":[25],"solution,":[26],"and":[27,79,91,120],"known":[29],"function.":[30],"This":[31],"simpler":[34],"model":[35],"problem":[36],"path":[39],"understanding":[41],"wave":[42],"field":[43],"singularities":[44],"caused":[45],"by":[46,77],"curve-shaped":[47],"scatterers":[48],"planar":[51],"domain.":[52],"prove":[54],"that":[55,101],"has":[56],"singularity":[58],"form":[61],",":[62],"Mellin":[66,90,103],"transform.":[67],"To":[68],"do":[69],"this,":[70],"we":[71],"use":[72],"specially":[73],"built":[74],"function":[75],"spaces":[76],"Zemanian,":[78],"these":[80],"allow":[81],"us":[82],"precisely":[84],"investigate":[85],"relationship":[87],"between":[88],"transforms.":[93],"Fourier":[94,108],"comes":[95],"into":[96],"play":[97],"sense":[100],"transform":[104,109],"simpy":[106],"locally":[112],"compact":[113],"Abelian":[114],"multiplicative":[115],"group":[116],"half-line,":[119],"as":[121],"more":[123],"familiar":[124],"operator,":[125],"it":[126],"guides":[127],"our":[128],"investigation.":[129]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}