{"title":"在正特征局部域上的索波列夫空间中的多级小波包","authors":"Ashish Pathak, Guru P. Singh","doi":"10.1007/s13370-024-01211-7","DOIUrl":null,"url":null,"abstract":"<div><p>The concepts of multiresolution analysis (MRA) and wavelets in Sobolev space over local fields of positive characteristic (<span>\\(H^s(\\mathbb {K})\\)</span>) are developed by Pathak and Singh [9]. In this paper, we constructed wavelet packets in Sobolev space <span>\\(H^s(\\mathbb {K})\\)</span> and derived their orthogonality at each level. By using convolution theory, an example of wavelet packets in <span>\\(H^s(\\mathbb {K})\\)</span> is presented</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multilevel wavelet packets in sobolev space over local fields of positive characteristic\",\"authors\":\"Ashish Pathak, Guru P. Singh\",\"doi\":\"10.1007/s13370-024-01211-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The concepts of multiresolution analysis (MRA) and wavelets in Sobolev space over local fields of positive characteristic (<span>\\\\(H^s(\\\\mathbb {K})\\\\)</span>) are developed by Pathak and Singh [9]. In this paper, we constructed wavelet packets in Sobolev space <span>\\\\(H^s(\\\\mathbb {K})\\\\)</span> and derived their orthogonality at each level. By using convolution theory, an example of wavelet packets in <span>\\\\(H^s(\\\\mathbb {K})\\\\)</span> is presented</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-08-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-024-01211-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-024-01211-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Multilevel wavelet packets in sobolev space over local fields of positive characteristic
The concepts of multiresolution analysis (MRA) and wavelets in Sobolev space over local fields of positive characteristic (\(H^s(\mathbb {K})\)) are developed by Pathak and Singh [9]. In this paper, we constructed wavelet packets in Sobolev space \(H^s(\mathbb {K})\) and derived their orthogonality at each level. By using convolution theory, an example of wavelet packets in \(H^s(\mathbb {K})\) is presented
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