{"id":"https://openalex.org/W2255767645","doi":"https://doi.org/10.1142/s0219691315500290","title":"Vector-valued nonuniform multiresolution analysis on local fields","display_name":"Vector-valued nonuniform multiresolution analysis on local fields","publication_year":2015,"publication_date":"2015-06-09","ids":{"openalex":"https://openalex.org/W2255767645","doi":"https://doi.org/10.1142/s0219691315500290","mag":"2255767645"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691315500290","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691315500290","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","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/A5037201286","display_name":"Firdous A. Shah","orcid":"https://orcid.org/0000-0001-8461-869X"},"institutions":[{"id":"https://openalex.org/I135388327","display_name":"University of Kashmir","ror":"https://ror.org/032xfst36","country_code":"IN","type":"education","lineage":["https://openalex.org/I135388327"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Firdous Ahmad Shah","raw_affiliation_strings":["Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India","institution_ids":["https://openalex.org/I135388327"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043368707","display_name":"M. Younus Bhat","orcid":"https://orcid.org/0000-0002-3369-0883"},"institutions":[{"id":"https://openalex.org/I145846420","display_name":"University of Jammu","ror":"https://ror.org/02retg991","country_code":"IN","type":"education","lineage":["https://openalex.org/I145846420"]},{"id":"https://openalex.org/I4210142231","display_name":"Central University of Jammu","ror":"https://ror.org/03nw1rg94","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210142231"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"M. Younus Bhat","raw_affiliation_strings":["Department of Mathematics, Central University of Jammu, Jammu-180011, Jammu and Kashmir, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Central University of Jammu, Jammu-180011, Jammu and Kashmir, India","institution_ids":["https://openalex.org/I145846420","https://openalex.org/I4210142231"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0679,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.863377,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":"04","first_page":"1550029","last_page":"1550029"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.995199978351593,"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":0.995199978351593,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9922000169754028,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9850000143051147,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.8228034973144531},{"id":"https://openalex.org/keywords/multiresolution-analysis","display_name":"Multiresolution analysis","score":0.819922924041748},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.6872150301933289},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.652831494808197},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6383928656578064},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6279048323631287},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.6224552989006042},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5050302147865295},{"id":"https://openalex.org/keywords/orthonormality","display_name":"Orthonormality","score":0.47250258922576904},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.4547301232814789},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.4428383708000183},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.44235771894454956},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44124457240104675},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3949007987976074},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3866320550441742},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36770564317703247},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32860350608825684},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.24388980865478516},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16839194297790527},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15325352549552917},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.15189480781555176},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08714953064918518},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08237531781196594}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.8228034973144531},{"id":"https://openalex.org/C121927907","wikidata":"https://www.wikidata.org/wiki/Q1952516","display_name":"Multiresolution analysis","level":5,"score":0.819922924041748},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.6872150301933289},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.652831494808197},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6383928656578064},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6279048323631287},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6224552989006042},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5050302147865295},{"id":"https://openalex.org/C92951342","wikidata":"https://www.wikidata.org/wiki/Q1411166","display_name":"Orthonormality","level":3,"score":0.47250258922576904},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.4547301232814789},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.4428383708000183},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.44235771894454956},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44124457240104675},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3949007987976074},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3866320550441742},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36770564317703247},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32860350608825684},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.24388980865478516},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16839194297790527},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15325352549552917},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.15189480781555176},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08714953064918518},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08237531781196594},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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:10.1142/s0219691315500290","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691315500290","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4399999976158142,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1483797993","https://openalex.org/W1972773636","https://openalex.org/W1972918357","https://openalex.org/W1980149518","https://openalex.org/W2006541359","https://openalex.org/W2013198648","https://openalex.org/W2014644430","https://openalex.org/W2042455747","https://openalex.org/W2043548573","https://openalex.org/W2046830589","https://openalex.org/W2050334122","https://openalex.org/W2054147619","https://openalex.org/W2059332474","https://openalex.org/W2062308863","https://openalex.org/W2077605849","https://openalex.org/W2087276022","https://openalex.org/W2092911074","https://openalex.org/W2094189485","https://openalex.org/W2111851797","https://openalex.org/W2170342375","https://openalex.org/W2334954345","https://openalex.org/W2567235724","https://openalex.org/W4249197173","https://openalex.org/W4292310788"],"related_works":["https://openalex.org/W2391983393","https://openalex.org/W1986893327","https://openalex.org/W1608252476","https://openalex.org/W2132871365","https://openalex.org/W2168986779","https://openalex.org/W2039167912","https://openalex.org/W2278852026","https://openalex.org/W2970039588","https://openalex.org/W3149039940","https://openalex.org/W1917817112"],"abstract_inverted_index":{"A":[0],"multiresolution":[1,46],"analysis":[2,47],"(MRA)":[3],"on":[4,38,133],"local":[5,134],"fields":[6,135],"of":[7,55,66,121,131],"positive":[8],"characteristic":[9],"was":[10],"defined":[11],"by":[12],"Shah":[13],"and":[14,42,87,96,101,115,124,153],"Abdullah":[15],"for":[16,118,128,151],"which":[17,25],"the":[18,35,50,67,119,129],"translation":[19],"set":[20,24],"is":[21,26,84,89],"a":[22,28,113,138],"discrete":[23],"not":[27],"group.":[29],"In":[30],"this":[31,39],"paper,":[32],"we":[33],"continue":[34],"study":[36],"based":[37],"nonstandard":[40],"setting":[41],"introduce":[43],"vector-valued":[44],"nonuniform":[45],"(VNUMRA)":[48],"where":[49,74],"associated":[51,122],"subspace":[52],"V":[53],"0":[54,109],"L":[56],"2":[57],"(K,":[58],"\u2102":[59],"M":[60],")":[61],"has":[62],"an":[63,85,90,126],"orthonormal":[64],"basis":[65],"form":[68],"{\u03a6":[69],"(x":[70],"-":[71],"\u03bb)}":[72],"\u03bb\u2208\u039b":[73],"\u039b":[75],"=":[76,103],"{0,":[77],"r/N}":[78],"+":[79],"\ud835\udcb5,":[80],"N":[81,97],"\u2265":[82],"1":[83],"integer":[86,92],"r":[88,95],"odd":[91],"such":[93],"that":[94],"are":[98],"relatively":[99],"prime":[100],"\ud835\udcb5":[102],"{u(n)":[104],":":[105],"n":[106],"\u2208":[107],"\u2115":[108],"}.":[110],"We":[111],"establish":[112],"necessary":[114],"sufficient":[116],"condition":[117],"existence":[120],"wavelets":[123],"derive":[125],"algorithm":[127],"construction":[130],"VNUMRA":[132],"starting":[136],"from":[137],"vector":[139],"refinement":[140],"mask":[141],"G(\u03be)":[142],"with":[143],"appropriate":[144],"conditions.":[145],"Further,":[146],"these":[147],"results":[148],"also":[149],"hold":[150],"Cantor":[152],"Vilenkin":[154],"groups.":[155]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
