{"id":"https://openalex.org/W2092998961","doi":"https://doi.org/10.1137/0153010","title":"Solution of Convolution Integral Equations by the Method of Differential Inversion","display_name":"Solution of Convolution Integral Equations by the Method of Differential Inversion","publication_year":1993,"publication_date":"1993-02-01","ids":{"openalex":"https://openalex.org/W2092998961","doi":"https://doi.org/10.1137/0153010","mag":"2092998961"},"language":"en","primary_location":{"id":"doi:10.1137/0153010","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0153010","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},"type":"article","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/A5082620363","display_name":"R. G. Hohlfeld","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"R. G. Hohlfeld","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041790665","display_name":"Jean I. F. King","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. I. F. King","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108831029","display_name":"Thomas W. Drueding","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. W. Drueding","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109075400","display_name":"G. Sandri","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. v. H. Sandri","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5082620363"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8697,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.91090869,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"53","issue":"1","first_page":"154","last_page":"167"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9988999962806702,"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":0.9988999962806702,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/mathematics","display_name":"Mathematics","score":0.7637819051742554},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6361381411552429},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.5161434412002563},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.4709511697292328},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.44717806577682495},{"id":"https://openalex.org/keywords/convolution-power","display_name":"Convolution power","score":0.4368632137775421},{"id":"https://openalex.org/keywords/series-expansion","display_name":"Series expansion","score":0.43312007188796997},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.42782270908355713},{"id":"https://openalex.org/keywords/multipole-expansion","display_name":"Multipole expansion","score":0.42564791440963745},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.3867202401161194},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.16849425435066223},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.10243231058120728}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7637819051742554},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6361381411552429},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.5161434412002563},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.4709511697292328},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.44717806577682495},{"id":"https://openalex.org/C86254553","wikidata":"https://www.wikidata.org/wiki/Q5166605","display_name":"Convolution power","level":5,"score":0.4368632137775421},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.43312007188796997},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.42782270908355713},{"id":"https://openalex.org/C52765159","wikidata":"https://www.wikidata.org/wiki/Q1027847","display_name":"Multipole expansion","level":2,"score":0.42564791440963745},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.3867202401161194},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.16849425435066223},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.10243231058120728},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0153010","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0153010","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W161930422","https://openalex.org/W588616829","https://openalex.org/W625004040","https://openalex.org/W1971918442","https://openalex.org/W1980983568","https://openalex.org/W2004917780","https://openalex.org/W2007287149","https://openalex.org/W2087093771","https://openalex.org/W2093671563","https://openalex.org/W2154231179","https://openalex.org/W2159419754","https://openalex.org/W2170120409","https://openalex.org/W2497066190","https://openalex.org/W2591313944","https://openalex.org/W2798409203","https://openalex.org/W3035162019","https://openalex.org/W3135227555","https://openalex.org/W4205109918","https://openalex.org/W4251100635","https://openalex.org/W4252975141"],"related_works":["https://openalex.org/W4387008893","https://openalex.org/W2043543980","https://openalex.org/W2135729712","https://openalex.org/W2032389377","https://openalex.org/W2061169599","https://openalex.org/W4381376912","https://openalex.org/W2392296723","https://openalex.org/W3186746902","https://openalex.org/W2561666027","https://openalex.org/W1978290145"],"abstract_inverted_index":{"In":[0,220],"this":[1,113,148,206],"paper,":[2],"a":[3,12,46,73,84,100,136,252],"method":[4,40,131,210],"called":[5],"\u201cdifferential":[6],"inversion\u201d":[7],"is":[8,30,67,83,90,132,153,161,203],"presented":[9,31],"for":[10,171],"solving":[11],"class":[13],"of":[14,20,24,48,51,99,117,129,143,147,158,167,174,190,195,229,245,254],"integral":[15,18],"equations":[16,19,197],"(Fredholm":[17],"the":[21,42,52,61,141,168,180,188,191,209,227],"first":[22],"kind)":[23],"convolution":[25,169,196],"form.":[26],"Differential":[27,88],"inversion":[28,86,89,182,194],"(DI)":[29],"as":[32,45],"an":[33,164],"alternative":[34],"to":[35,69,92,95,150,162,214,251],"Fourier":[36,241],"transform":[37],"methods.":[38],"The":[39,55,108,145,177,193,243],"expresses":[41],"unknown":[43],"function":[44],"series":[47,183],"successive":[49],"derivatives":[50],"known":[53],"function.":[54],"known-unknown":[56],"functions":[57],"are":[58,115,224,249],"evaluated":[59],"at":[60,102],"same":[62],"point.":[63],"This":[64],"new":[65],"expansion":[66,82,98],"not":[68],"be":[70,93,185,212,237],"confused":[71],"with":[72,198,217],"Taylor":[74,81],"expansion,":[75],"although":[76],"we":[77,120],"show":[78],"that":[79,133,235],"every":[80],"differential":[85,181],"expansion.":[87],"shown":[91],"related":[94],"Gauss\u2019s":[96],"multipole":[97],"field":[101,139,149,152],"large":[103],"distances":[104],"from":[105,187],"its":[106],"source.":[107],"fundamental":[109],"mathematical":[110],"objects":[111],"in":[112,140,179,205,226,232,257],"theory":[114],"generalizations":[116],"distributions,":[118],"which":[119],"term":[121],"\u201cgeneralized":[122],"distributions\u201d":[123],"or":[124],"\u201chyperdistributions.\u201d":[125],"An":[126],"important":[127],"feature":[128],"our":[130,159,175],"convolutions":[134],"form":[135],"closed":[137],"algebraic":[138],"space":[142,228],"hyperdistributions.":[144],"relation":[146],"Mikusi\u0144ski\u2019s":[151],"discussed.":[154],"A":[155],"major":[156],"result":[157],"analysis":[160],"give":[163],"explicit":[165],"construction":[166],"inverse":[170,266],"any":[172,215],"element":[173],"field.":[176],"coefficients":[178],"may":[184,211],"computed":[186],"moments":[189],"kernel.":[192],"exponential":[199],"and":[200,264],"Gaussian":[201],"kernels":[202,246],"demonstrated":[204],"paper":[207],"(although":[208],"applied":[213],"kernel":[216],"finite":[218],"moments).":[219],"particular,":[221],"unique":[222],"solutions":[223],"obtained":[225],"hyperdistributions,":[230],"even":[231],"those":[233],"cases":[234],"cannot":[236],"represented":[238],"by":[239],"convergent":[240],"integrals.":[242],"choices":[244],"made":[247],"here":[248],"relevant":[250],"number":[253],"physical":[255],"problems":[256],"signal":[258],"processing,":[259,261],"image":[260],"radiative":[262],"transfer,":[263],"other":[265],"problems.":[267]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}