{"id":"https://openalex.org/W4409508412","doi":"https://doi.org/10.3390/axioms14040302","title":"An Axiomatic Approach to Mild Distributions","display_name":"An Axiomatic Approach to Mild Distributions","publication_year":2025,"publication_date":"2025-04-16","ids":{"openalex":"https://openalex.org/W4409508412","doi":"https://doi.org/10.3390/axioms14040302"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14040302","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040302","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","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/axioms14040302","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016044961","display_name":"Hans G. Feichtinger","orcid":"https://orcid.org/0000-0002-9927-0742"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]},{"id":"https://openalex.org/I2800119247","display_name":"Acoustics Research Institute","ror":"https://ror.org/04jd9ff79","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I2800119247"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Hans G. Feichtinger","raw_affiliation_strings":["Acoustic Research Institute OEAW, 1010 Vienna, Austria","Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Acoustic Research Institute OEAW, 1010 Vienna, Austria","institution_ids":["https://openalex.org/I2800119247"]},{"raw_affiliation_string":"Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016044961"],"corresponding_institution_ids":["https://openalex.org/I129774422","https://openalex.org/I2800119247"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12980442,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"4","first_page":"302","last_page":"302"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9984999895095825,"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":0.9984999895095825,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9945999979972839,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9745000004768372,"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/axiomatic-system","display_name":"Axiomatic system","score":0.5248503684997559},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5066159963607788},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37648433446884155},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35385414958000183},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06926065683364868}],"concepts":[{"id":"https://openalex.org/C125773388","wikidata":"https://www.wikidata.org/wiki/Q792542","display_name":"Axiomatic system","level":3,"score":0.5248503684997559},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5066159963607788},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37648433446884155},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35385414958000183},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06926065683364868}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14040302","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040302","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b6a6565b9dcc478a8bf2a1aa27b5252f","is_oa":true,"landing_page_url":"https://doaj.org/article/b6a6565b9dcc478a8bf2a1aa27b5252f","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 4, p 302 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14040302","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040302","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W112412991","https://openalex.org/W621920399","https://openalex.org/W1013287737","https://openalex.org/W1553283060","https://openalex.org/W1605417594","https://openalex.org/W1974324069","https://openalex.org/W1976869454","https://openalex.org/W1981479929","https://openalex.org/W1992791816","https://openalex.org/W1998201449","https://openalex.org/W2010386221","https://openalex.org/W2033758190","https://openalex.org/W2043437348","https://openalex.org/W2048032666","https://openalex.org/W2062322118","https://openalex.org/W2082165232","https://openalex.org/W2083929598","https://openalex.org/W2087502041","https://openalex.org/W2088623638","https://openalex.org/W2097916195","https://openalex.org/W2104873039","https://openalex.org/W2126405614","https://openalex.org/W2227420806","https://openalex.org/W2324513440","https://openalex.org/W2408848726","https://openalex.org/W2414887269","https://openalex.org/W2488522998","https://openalex.org/W2530137078","https://openalex.org/W2740215163","https://openalex.org/W2745174020","https://openalex.org/W2788260027","https://openalex.org/W2962930505","https://openalex.org/W2963213835","https://openalex.org/W3008254177","https://openalex.org/W3008427995","https://openalex.org/W3033103267","https://openalex.org/W3103402207","https://openalex.org/W3183943402","https://openalex.org/W4210417065","https://openalex.org/W4229765860","https://openalex.org/W4229923956","https://openalex.org/W4248262852","https://openalex.org/W4253840677","https://openalex.org/W4295135457","https://openalex.org/W4302204372","https://openalex.org/W4367669901","https://openalex.org/W4385490844","https://openalex.org/W4390575197","https://openalex.org/W4405373225","https://openalex.org/W6659029531"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1771651560","https://openalex.org/W2386897142","https://openalex.org/W4300725361","https://openalex.org/W1605727975","https://openalex.org/W4232127999","https://openalex.org/W4289976264","https://openalex.org/W3101572115","https://openalex.org/W2127270425","https://openalex.org/W329313523"],"abstract_inverted_index":{"The":[0],"Banach":[1,66,72,184],"Gelfand":[2,35,73,185],"Triple":[3,36],"(S0,L2,S0\u2032)":[4],"consists":[5],"of":[6,14,25,43,49,70,81,103,112,129,182,202,206,222,240,252,261,269],"the":[7,17,23,29,41,47,62,78,100,110,134,143,165,168,211,219,228,241,253],"Feichtinger":[8],"algebra":[9],"S0(Rd)":[10,217],"as":[11,22,133,196],"a":[12,71,139,178,250,258,267],"space":[13,19,24,32,231],"test":[15],"functions,":[16],"dual":[18,230],"S0\u2032(Rd),":[20],"known":[21],"mild":[26],"distributions,":[27],"and":[28,58,125,147,159,265],"intermediate":[30],"Hilbert":[31,83],"L2(Rd).":[33],"This":[34,247],"is":[37,218,227],"very":[38,95],"useful":[39],"for":[40,54,155,243],"description":[42,128],"mathematical":[44,113],"problems":[45],"in":[46,75,109,121,164,210],"area":[48],"time-frequency":[50,148],"analysis,":[51,149],"but":[52,119,150],"also":[53,120,151],"classical":[55,130],"Fourier":[56,146,197],"analysis":[57],"engineering":[59],"applications.":[60],"Because":[61],"involved":[63],"spaces":[64],"are":[65],"spaces,":[67,84,235],"we":[68,171],"speak":[69],"Triple,":[74],"contrast":[76],"to":[77,116,141,191],"widespread":[79],"concept":[80],"rigged":[82],"which":[85,236],"usually":[86],"involve":[87],"nuclear":[88],"Frechet":[89],"spaces.":[90],"Still,":[91],"both":[92],"concepts":[93],"serve":[94],"similar":[96,183],"purposes.":[97],"Based":[98],"on":[99],"manifold":[101],"properties":[102,194,255],"S0(Rd),":[104],"it":[105],"has":[106],"found":[107],"applications":[108],"derivation":[111],"statements":[114],"related":[115],"Gabor":[117],"Analysis":[118],"providing":[122],"an":[123],"alternative":[124],"more":[126],"lucid":[127],"results,":[131],"such":[132,195],"Shannon":[135],"sampling":[136],"theory,":[137],"with":[138],"potential":[140],"renew":[142],"way":[144],"how":[145],"signal":[152],"processing":[153],"courses":[154],"engineers":[156],"(or":[157],"physicists":[158],"mathematicians)":[160],"could":[161,176],"be":[162,238],"taught":[163],"future.":[166],"In":[167],"present":[169],"study,":[170],"will":[172],"demonstrate":[173],"that":[174,216],"one":[175,189,239],"choose":[177],"relatively":[179,262],"large":[180],"variety":[181],"Triples,":[186],"even":[187],"if":[188],"wants":[190],"include":[192],"key":[193],"invariance":[198],"(an":[199],"extended":[200],"version":[201],"Plancherel\u2019s":[203],"Theorem).":[204],"Some":[205],"them":[207],"appeared":[208],"naturally":[209],"literature.":[212],"It":[213],"turns":[214],"out,":[215],"smallest":[220],"member":[221],"this":[223],"family.":[224],"Consequently":[225],"S0\u2032(Rd)":[226],"largest":[229],"among":[232],"all":[233],"these":[234,273],"may":[237],"reasons":[242],"its":[244],"universal":[245],"usefulness.":[246],"article":[248],"provides":[249],"study":[251],"basic":[254,274],"following":[256],"from":[257],"short":[259],"list":[260,268],"simple":[263],"assumptions":[264],"gives":[266],"non-trivial":[270],"examples":[271],"satisfying":[272],"axioms.":[275]},"counts_by_year":[],"updated_date":"2026-02-27T16:54:17.756197","created_date":"2025-10-10T00:00:00"}
