{"id":"https://openalex.org/W1972918357","doi":"https://doi.org/10.1142/s021969131250018x","title":"WAVELETS ASSOCIATED WITH NONUNIFORM MULTIRESOLUTION ANALYSIS ON POSITIVE HALF-LINE","display_name":"WAVELETS ASSOCIATED WITH NONUNIFORM MULTIRESOLUTION ANALYSIS ON POSITIVE HALF-LINE","publication_year":2012,"publication_date":"2012-02-15","ids":{"openalex":"https://openalex.org/W1972918357","doi":"https://doi.org/10.1142/s021969131250018x","mag":"1972918357"},"language":"en","primary_location":{"id":"doi:10.1142/s021969131250018x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021969131250018x","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/A5114237946","display_name":"Meenakshi Meenakshi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"MEENAKSHI","raw_affiliation_strings":["Department of Mathematics, Lajpat Rai DAV College, Jagraon, Punjab, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Lajpat Rai DAV College, Jagraon, Punjab, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112459082","display_name":"Pammy Manchanda","orcid":null},"institutions":[{"id":"https://openalex.org/I165682329","display_name":"Guru Nanak Dev University","ror":"https://ror.org/05ghzpa93","country_code":"IN","type":"education","lineage":["https://openalex.org/I165682329"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"P. MANCHANDA","raw_affiliation_strings":["Department of Mathematics, Guru Nanak Dev University, Amritsar, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Guru Nanak Dev University, Amritsar, India","institution_ids":["https://openalex.org/I165682329"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073901040","display_name":"Abul Hasan Siddiqi","orcid":null},"institutions":[{"id":"https://openalex.org/I47818738","display_name":"Sultan Qaboos University","ror":"https://ror.org/04wq8zb47","country_code":"OM","type":"education","lineage":["https://openalex.org/I47818738"]},{"id":"https://openalex.org/I74885063","display_name":"Sharda University","ror":"https://ror.org/03b6ffh07","country_code":"IN","type":"education","lineage":["https://openalex.org/I74885063"]}],"countries":["IN","OM"],"is_corresponding":false,"raw_author_name":"A. H. SIDDIQI","raw_affiliation_strings":["School of Engineering and Technology, Sharda University, Greater Noida, India","Sultan Qaboos University, Muscat, Oman"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering and Technology, Sharda University, Greater Noida, India","institution_ids":["https://openalex.org/I74885063"]},{"raw_affiliation_string":"Sultan Qaboos University, Muscat, Oman","institution_ids":["https://openalex.org/I47818738"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9065,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.8690208,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"10","issue":"02","first_page":"1250018","last_page":"1250018"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9988999962806702,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.979200005531311,"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/multiresolution-analysis","display_name":"Multiresolution analysis","score":0.8939875364303589},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.7682031393051147},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.7585391998291016},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6011127829551697},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5788455605506897},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.4833466708660126},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4694000780582428},{"id":"https://openalex.org/keywords/orthonormality","display_name":"Orthonormality","score":0.45687001943588257},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4415794014930725},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3818431496620178},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36524197459220886},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.3182790279388428},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20158180594444275},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16624033451080322},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.13772904872894287},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07676181197166443}],"concepts":[{"id":"https://openalex.org/C121927907","wikidata":"https://www.wikidata.org/wiki/Q1952516","display_name":"Multiresolution analysis","level":5,"score":0.8939875364303589},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.7682031393051147},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.7585391998291016},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6011127829551697},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5788455605506897},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4833466708660126},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4694000780582428},{"id":"https://openalex.org/C92951342","wikidata":"https://www.wikidata.org/wiki/Q1411166","display_name":"Orthonormality","level":3,"score":0.45687001943588257},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4415794014930725},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3818431496620178},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36524197459220886},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.3182790279388428},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20158180594444275},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16624033451080322},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.13772904872894287},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07676181197166443},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021969131250018x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021969131250018x","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W86370709","https://openalex.org/W1552503961","https://openalex.org/W1980149518","https://openalex.org/W2007565866","https://openalex.org/W2013198648","https://openalex.org/W2018580045","https://openalex.org/W2046830589","https://openalex.org/W2092911074","https://openalex.org/W2125135910","https://openalex.org/W2154003217","https://openalex.org/W2159337174","https://openalex.org/W2160881571","https://openalex.org/W2581433367","https://openalex.org/W4249197173","https://openalex.org/W4255272544"],"related_works":["https://openalex.org/W2013801824","https://openalex.org/W1496788307","https://openalex.org/W1591253575","https://openalex.org/W2149054915","https://openalex.org/W1529452180","https://openalex.org/W2138614992","https://openalex.org/W2112487673","https://openalex.org/W2013322017","https://openalex.org/W614741956","https://openalex.org/W1573087379"],"abstract_inverted_index":{"Gabardo":[0],"and":[1,23,39,109,126,131,144,153],"Nashed":[2],"have":[3,53],"studied":[4],"nonuniform":[5,56,162],"multiresolution":[6,32,57,163],"analysis":[7,33,58,164],"based":[8],"on":[9,34,46,59,165],"the":[10,29,41,55,82,87,135,142,148,155,161,166],"theory":[11],"of":[12,18,31,67,79,81,86,137,150,157],"spectral":[13],"pairs":[14],"in":[15],"a":[16,77],"series":[17],"papers,":[19],"see":[20],"Refs.":[21],"4":[22],"5.":[24],"Farkov,":[25],"3":[26],"has":[27,73],"extended":[28],"notion":[30],"locally":[35],"compact":[36],"Abelian":[37],"groups":[38],"constructed":[40],"compactly":[42],"supported":[43],"orthogonal":[44],"p-wavelets":[45],"L":[47,68],"2":[48,69],"(\u211d":[49,70],"+":[50,71,93,96,100,102,133],").":[51],"We":[52,140],"considered":[54],"positive":[60,167],"half-line.":[61,168],"The":[62],"associated":[63,151],"subspace":[64],"V":[65],"0":[66],")":[72],"an":[74,112],"orthonormal":[75],"basis,":[76],"collection":[78],"translates":[80],"scaling":[83],"function":[84],"\u03c6":[85],"form":[88],"{\u03c6(x":[89],"\u2296":[90],"\u03bb)}":[91],"\u03bb\u2208\u039b":[92],"where":[94],"\u039b":[95],"=":[97],"{0,":[98],"r/N}":[99],"\u2124":[101,132],",":[103],"N":[104,127],"&gt;":[105],"1":[106,116,122],"(an":[107],"integer)":[108],"r":[110,118,125],"is":[111,134],"odd":[113],"integer":[114],"with":[115],"\u2264":[117,119],"2N":[120],"-":[121],"such":[123],"that":[124],"are":[128],"relatively":[129],"prime":[130],"set":[136],"non-negative":[138],"integers.":[139],"find":[141],"necessary":[143],"sufficient":[145],"condition":[146,159],"for":[147,160],"existence":[149],"wavelets":[152],"derive":[154],"analogue":[156],"Cohen's":[158]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
