{"id":"https://openalex.org/W4412456807","doi":"https://doi.org/10.3390/axioms14070533","title":"Clifford Distributions Revisited","display_name":"Clifford Distributions Revisited","publication_year":2025,"publication_date":"2025-07-14","ids":{"openalex":"https://openalex.org/W4412456807","doi":"https://doi.org/10.3390/axioms14070533"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14070533","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070533","pdf_url":"https://www.mdpi.com/2075-1680/14/7/533/pdf?version=1752499002","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://www.mdpi.com/2075-1680/14/7/533/pdf?version=1752499002","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043439059","display_name":"Fred Brackx","orcid":"https://orcid.org/0000-0002-1849-8826"},"institutions":[{"id":"https://openalex.org/I2802067006","display_name":"Research Foundation - Flanders","ror":"https://ror.org/03qtxy027","country_code":"BE","type":"government","lineage":["https://openalex.org/I2802067006"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Fred Brackx","raw_affiliation_strings":["Clifford Research Group, Foundations Lab, Department of Electronics and Information Systems, Faculty of Engineering and Architecture, Ghent University (Belgium), B-9000 Gent, Belgium"],"affiliations":[{"raw_affiliation_string":"Clifford Research Group, Foundations Lab, Department of Electronics and Information Systems, Faculty of Engineering and Architecture, Ghent University (Belgium), B-9000 Gent, Belgium","institution_ids":["https://openalex.org/I2802067006"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043439059"],"corresponding_institution_ids":["https://openalex.org/I2802067006"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.26372734,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"7","first_page":"533","last_page":"533"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9998999834060669,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9998999834060669,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9975000023841858,"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/T13234","display_name":"advanced mathematical theories","score":0.9854999780654907,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.6368728876113892},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.6071628332138062},{"id":"https://openalex.org/keywords/scalar-multiplication","display_name":"Scalar multiplication","score":0.577656626701355},{"id":"https://openalex.org/keywords/clifford-algebra","display_name":"Clifford algebra","score":0.5688413381576538},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.548287570476532},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.48088887333869934},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4578416049480438},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4322047531604767},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43178656697273254},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.4174595773220062},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.416848361492157},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33957093954086304},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.30744290351867676},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14901036024093628},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12822186946868896}],"concepts":[{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6368728876113892},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.6071628332138062},{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.577656626701355},{"id":"https://openalex.org/C100856211","wikidata":"https://www.wikidata.org/wiki/Q674689","display_name":"Clifford algebra","level":3,"score":0.5688413381576538},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.548287570476532},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.48088887333869934},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4578416049480438},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4322047531604767},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43178656697273254},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.4174595773220062},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.416848361492157},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33957093954086304},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30744290351867676},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14901036024093628},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12822186946868896},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms14070533","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070533","pdf_url":"https://www.mdpi.com/2075-1680/14/7/533/pdf?version=1752499002","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:archive.ugent.be:01K1T5FA8RYFXAW4G5ZB1NZ7AG","is_oa":true,"landing_page_url":"http://hdl.handle.net/1854/LU-01K1T5FA8RYFXAW4G5ZB1NZ7AG","pdf_url":"https://biblio.ugent.be/publication/01K1T5FA8RYFXAW4G5ZB1NZ7AG/file/01K1T5HCZS261K165V5QZS0A3A.pdf","source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"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":"ISSN: 2075-1680","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:doaj.org/article:2718672d6e394881a33db0dd734402b5","is_oa":true,"landing_page_url":"https://doaj.org/article/2718672d6e394881a33db0dd734402b5","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 7, p 533 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14070533","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070533","pdf_url":"https://www.mdpi.com/2075-1680/14/7/533/pdf?version=1752499002","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":[{"id":"https://metadata.un.org/sdg/11","score":0.41999998688697815,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412456807.pdf","grobid_xml":"https://content.openalex.org/works/W4412456807.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1578753167","https://openalex.org/W1971129037","https://openalex.org/W1972513338","https://openalex.org/W1978042886","https://openalex.org/W2022762959","https://openalex.org/W2023053598","https://openalex.org/W2024666396","https://openalex.org/W2283390586","https://openalex.org/W2316624819","https://openalex.org/W2477819211","https://openalex.org/W2996245578","https://openalex.org/W3099064701","https://openalex.org/W3099137090","https://openalex.org/W3106030560","https://openalex.org/W4244455810","https://openalex.org/W4294624663","https://openalex.org/W4404554362","https://openalex.org/W6635532689"],"related_works":["https://openalex.org/W2034604290","https://openalex.org/W2867317277","https://openalex.org/W1576294153","https://openalex.org/W2078886092","https://openalex.org/W2362283711","https://openalex.org/W2002792918","https://openalex.org/W2360049128","https://openalex.org/W1485234189","https://openalex.org/W4386773944","https://openalex.org/W2495172928"],"abstract_inverted_index":{"In":[0],"the":[1,36,44,69,74,87],"framework":[2],"of":[3,13,18,62,76,80,95],"harmonic":[4],"and":[5,39,41,82],"Clifford":[6],"analysis,":[7],"specific":[8],"distributions":[9,88],"in":[10,103],"Euclidean":[11],"space":[12,61],"arbitrary":[14],"dimension,":[15],"which":[16],"are":[17,24],"particular":[19],"importance":[20],"for":[21],"theoretical":[22],"physics,":[23],"once":[25],"more":[26],"thoroughly":[27],"studied.":[28],"Indeed,":[29],"actions":[30,75],"involving":[31],"spherical":[32],"coordinates,":[33],"such":[34],"as":[35,98],"radial":[37,45],"derivative":[38],"multiplication":[40],"division":[42],"by":[43,100],"distance,":[46],"only":[47],"make":[48],"sense":[49],"when":[50],"considering":[51],"so-called":[52],"signumdistributions,":[53,73],"that":[54],"is,":[55],"bounded":[56],"linear":[57],"functionals":[58],"on":[59,86],"a":[60,66,77,93],"test":[63],"functions":[64],"showing":[65],"singularity":[67],"at":[68],"origin.":[70],"Introducing":[71],"these":[72],"whole":[78],"series":[79],"scalar":[81],"vectorial":[83],"differential":[84],"operators":[85],"under":[89],"consideration,":[90],"lead":[91],"to":[92],"number":[94],"surprising":[96],"results,":[97],"illustrated":[99],"some":[101],"examples":[102],"three-dimensional":[104],"mathematical":[105],"physics.":[106]},"counts_by_year":[],"updated_date":"2026-03-08T08:50:53.379069","created_date":"2025-10-10T00:00:00"}