{"title":"Schwartz调和分布的连续小波变换","authors":"J. Pandey, S. K. Upadhyay","doi":"10.1080/25742558.2019.1623647","DOIUrl":null,"url":null,"abstract":"Abstract The continuous wavelet transform of Schwartz tempered distributions is investigated and derive the corresponding wavelet inversion formula (valid modulo a constant-tempered distribution) interpreting convergence in . But uniqueness theorem for the present wavelet inversion formula is valid for the space obtained by filtering (deleting) (i) all non-zero constant distributions from the space , (ii) all non-zero constants that appear with a distribution as a union. As an example, in considering the distribution we would omit 1 and retain only . The wavelet kernel under consideration for determining the wavelet transform are those wavelets whose all the moments are non-zero. As an example, is such a wavelet. is an arbitrary constant. There exist many other classes of such wavelets. In our analysis, we do not use a wavelet kernel having any of its moments zero.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1623647","citationCount":"2","resultStr":"{\"title\":\"Continuous wavelet transform of Schwartz tempered distributions\",\"authors\":\"J. Pandey, S. K. Upadhyay\",\"doi\":\"10.1080/25742558.2019.1623647\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The continuous wavelet transform of Schwartz tempered distributions is investigated and derive the corresponding wavelet inversion formula (valid modulo a constant-tempered distribution) interpreting convergence in . But uniqueness theorem for the present wavelet inversion formula is valid for the space obtained by filtering (deleting) (i) all non-zero constant distributions from the space , (ii) all non-zero constants that appear with a distribution as a union. As an example, in considering the distribution we would omit 1 and retain only . The wavelet kernel under consideration for determining the wavelet transform are those wavelets whose all the moments are non-zero. As an example, is such a wavelet. is an arbitrary constant. There exist many other classes of such wavelets. In our analysis, we do not use a wavelet kernel having any of its moments zero.\",\"PeriodicalId\":92618,\"journal\":{\"name\":\"Cogent mathematics & statistics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/25742558.2019.1623647\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cogent mathematics & statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/25742558.2019.1623647\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cogent mathematics & statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/25742558.2019.1623647","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Continuous wavelet transform of Schwartz tempered distributions
Abstract The continuous wavelet transform of Schwartz tempered distributions is investigated and derive the corresponding wavelet inversion formula (valid modulo a constant-tempered distribution) interpreting convergence in . But uniqueness theorem for the present wavelet inversion formula is valid for the space obtained by filtering (deleting) (i) all non-zero constant distributions from the space , (ii) all non-zero constants that appear with a distribution as a union. As an example, in considering the distribution we would omit 1 and retain only . The wavelet kernel under consideration for determining the wavelet transform are those wavelets whose all the moments are non-zero. As an example, is such a wavelet. is an arbitrary constant. There exist many other classes of such wavelets. In our analysis, we do not use a wavelet kernel having any of its moments zero.