{"id":"https://openalex.org/W1993327752","doi":"https://doi.org/10.1137/s0895479894262327","title":"On Construction of a Family of Smooth Nonseparable Prewavelets via Infinite Products of Triangularizable Matrices","display_name":"On Construction of a Family of Smooth Nonseparable Prewavelets via Infinite Products of Triangularizable Matrices","publication_year":1998,"publication_date":"1998-10-01","ids":{"openalex":"https://openalex.org/W1993327752","doi":"https://doi.org/10.1137/s0895479894262327","mag":"1993327752"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479894262327","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479894262327","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5032911682","display_name":"M\u00f3hsen Maesumi","orcid":"https://orcid.org/0000-0001-6458-4816"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mohsen Maesumi","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032911682"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12669443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"4","first_page":"1005","last_page":"1026"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9930999875068665,"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/T11659","display_name":"Advanced Image Fusion Techniques","score":0.9817000031471252,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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":0.8959958553314209},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.583843469619751},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5692786574363708},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5645015239715576},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.48265010118484497},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.46347177028656006},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.43033367395401},{"id":"https://openalex.org/keywords/dilation","display_name":"Dilation (metric space)","score":0.4219779074192047},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40066462755203247},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3651367425918579},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32144230604171753},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20998799800872803}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8959958553314209},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.583843469619751},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5692786574363708},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5645015239715576},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.48265010118484497},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.46347177028656006},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.43033367395401},{"id":"https://openalex.org/C2780757906","wikidata":"https://www.wikidata.org/wiki/Q5276676","display_name":"Dilation (metric space)","level":2,"score":0.4219779074192047},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40066462755203247},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3651367425918579},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32144230604171753},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20998799800872803},{"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/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479894262327","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479894262327","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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":17,"referenced_works":["https://openalex.org/W14246339","https://openalex.org/W1978558994","https://openalex.org/W1980695038","https://openalex.org/W1981798791","https://openalex.org/W2003989039","https://openalex.org/W2017721907","https://openalex.org/W2020068051","https://openalex.org/W2030934791","https://openalex.org/W2032326995","https://openalex.org/W2041752335","https://openalex.org/W2062024414","https://openalex.org/W2079227289","https://openalex.org/W2098914003","https://openalex.org/W2103966928","https://openalex.org/W2341241031","https://openalex.org/W4255272544","https://openalex.org/W4297562995"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4285277090","https://openalex.org/W4390756076"],"abstract_inverted_index":{"Infinite":[0],"products":[1,27],"of":[2,12,21,23,40,43,106,114,137,143,149,154,159,162,171],"matrices":[3,109],"arise":[4],"in":[5,112],"many":[6],"areas,":[7],"such":[8],"as":[9],"the":[10,36,56,80,127,141,144,157,163,169,175],"study":[11],"subdivision":[13],"and":[14,19,38,74,85,124],"interpolation":[15,136],"schemes,":[16],"Markov":[17],"chains,":[18],"construction":[20],"wavelets":[22],"compact":[24],"support.":[25],"These":[26,99],"are":[28,97,101,119,132],"used":[29],"here":[30],"to":[31,121,126,174],"give":[32],"sufficient":[33,86,166],"conditions":[34,87,100,167],"for":[35,168],"continuity":[37],"differentiability":[39],"a":[41,92],"class":[42],"rectangular":[44],"compactly":[45],"supported":[46],"nonseparable":[47],"N-dimensional":[48],"prewavelets":[49],"or":[50],"scaling":[51,94],"functions.":[52],"This":[53],"paper":[54],"considers":[55],"dilation":[57,176],"equation":[58],"$\\phi(X)=\\sum_K":[59],"C_K":[60],"\\phi(2X-K)$,":[61],"where":[62,130],"$K\\in":[63],"\\{0,":[64],"\\ldots,":[65],"m\\}^N$,":[66],"$\\phi":[67],":":[68],"{\\cal":[69,72,77],"R}^N":[70],"\\to":[71],"R}$,":[73],"$C_K":[75],"\\in":[76],"R}$.":[78],"First,":[79],"one-dimensional":[81],"case":[82,129],"is":[83],"studied,":[84],"on":[88,103,152,156],"CK,":[89],"which":[90],"guarantee":[91],"continuous":[93],"function":[95],"$\\phi(X)$,":[96],"given.":[98],"based":[102,151],"simultaneous":[104],"triangularizability":[105],"two":[107],"special":[108],"with":[110],"entries":[111],"terms":[113],"CK.":[115],"Then,":[116],"these":[117],"results":[118],"generalized":[120],"N":[122],"dimensions":[123],"applied":[125],"particular":[128],"CK's":[131,155],"obtained":[133],"by":[134],"binomial":[135],"their":[138],"values":[139],"at":[140],"corners":[142,158],"N-cube,":[145],"$\\{0,m\\}^N$.":[146],"A":[147],"set":[148],"inequalities,":[150],"sums":[153],"various":[160],"faces":[161],"N-cube":[164],"gives":[165],"existence":[170],"smooth":[172],"solutions":[173],"equation.":[177]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
