{"id":"https://openalex.org/W1998315126","doi":"https://doi.org/10.1142/s021969130800232x","title":"SAMPLING EXPANSION IN SHIFT INVARIANT SPACES","display_name":"SAMPLING EXPANSION IN SHIFT INVARIANT SPACES","publication_year":2008,"publication_date":"2008-03-01","ids":{"openalex":"https://openalex.org/W1998315126","doi":"https://doi.org/10.1142/s021969130800232x","mag":"1998315126"},"language":"en","primary_location":{"id":"doi:10.1142/s021969130800232x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021969130800232x","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/A5028181552","display_name":"J. M. Kim","orcid":null},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"J. M. KIM","raw_affiliation_strings":["Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Republic of Korea","Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Republic of Korea","institution_ids":["https://openalex.org/I157485424"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea#TAB#","institution_ids":["https://openalex.org/I157485424"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050777309","display_name":"K.H. Kwon","orcid":"https://orcid.org/0000-0002-1025-9580"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"K. H. KWON","raw_affiliation_strings":["Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Republic of Korea","Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Republic of Korea","institution_ids":["https://openalex.org/I157485424"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea#TAB#","institution_ids":["https://openalex.org/I157485424"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028181552"],"corresponding_institution_ids":["https://openalex.org/I157485424"],"apc_list":null,"apc_paid":null,"fwci":4.7602,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.94905188,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"06","issue":"02","first_page":"223","last_page":"248"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9995999932289124,"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":0.9995999932289124,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9882000088691711,"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":0.9675999879837036,"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/mathematics","display_name":"Mathematics","score":0.759599506855011},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.6285693049430847},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5584179759025574},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.546751856803894},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5091955065727234},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44341588020324707},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3913591504096985},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37868255376815796},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.330657958984375},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.09820356965065002},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08889347314834595}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.759599506855011},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.6285693049430847},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5584179759025574},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.546751856803894},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5091955065727234},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44341588020324707},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3913591504096985},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37868255376815796},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.330657958984375},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.09820356965065002},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08889347314834595},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021969130800232x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021969130800232x","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":[{"id":"https://openalex.org/F4320322348","display_name":"Korea Science and Engineering Foundation","ror":"https://ror.org/013aysd81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W224962721","https://openalex.org/W637373309","https://openalex.org/W1980365685","https://openalex.org/W1998298110","https://openalex.org/W2008844048","https://openalex.org/W2044350368","https://openalex.org/W2084633773","https://openalex.org/W2100653569","https://openalex.org/W2102897204","https://openalex.org/W2118726884","https://openalex.org/W2164759854","https://openalex.org/W2171435376","https://openalex.org/W4256555983","https://openalex.org/W4292170079","https://openalex.org/W4388315674"],"related_works":["https://openalex.org/W1980381208","https://openalex.org/W2364594919","https://openalex.org/W2167092671","https://openalex.org/W1861706286","https://openalex.org/W2219338811","https://openalex.org/W2149583853","https://openalex.org/W2143002539","https://openalex.org/W2130386332","https://openalex.org/W1120847856","https://openalex.org/W4293472652"],"abstract_inverted_index":{"For":[0],"any":[1],"\u03d5(t)":[2,34],"in":[3,96],"L":[4,16,97,107],"2":[5,17,98,108],"(\u211d),":[6],"let":[7],"V(\u03d5)":[8,50,77],"be":[9],"the":[10,84],"closed":[11],"shift":[12],"invariant":[13],"subspace":[14,105],"of":[15,30,42,83,106],"(\u211d)":[18,99],"spanned":[19],"by":[20],"integer":[21],"translates":[22],"{\u03d5(t":[23],"-":[24],"n)":[25],":":[26],"n":[27],"\u2208":[28],"\u2124}":[29],"\u03d5(t).":[31],"Assuming":[32],"that":[33,100],"is":[35],"a":[36,39,52,69,90,94,103],"frame":[37],"or":[38,68],"Riesz":[40],"generator":[41],"V(\u03d5),":[43],"we":[44],"first":[45],"find":[46,59,89],"conditions":[47,63],"under":[48,64],"which":[49,65],"becomes":[51],"reproducing":[53],"kernel":[54],"Hilbert":[55],"space.":[56],"We":[57,87],"then":[58],"necessary":[60],"and":[61,78],"sufficient":[62,91],"an":[66],"irregular":[67],"regular":[70],"shifted":[71],"sampling":[72,85,104],"expansion":[73],"formula":[74],"holds":[75],"on":[76],"obtain":[79],"truncation":[80],"error":[81],"estimates":[82],"series.":[86],"also":[88,114],"condition":[92],"for":[93],"function":[95],"belongs":[101],"to":[102],"(\u211d).":[109],"Several":[110],"illustrating":[111],"examples":[112],"are":[113],"provided.":[115]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}