{"title":"圆上的Gabor变换","authors":"K. Fujita","doi":"10.1109/ICWAPR.2014.6961302","DOIUrl":null,"url":null,"abstract":"In [2] and [3], we considered the Gabor transform of analytic functionals on the sphere in general dimension and we expressed it by a series expansion with the spherical harmonics and the Bessel functions. In this paper, following our previous results, we will consider the Gabor transform of analytic functionals, especially of square integrable functions on the circle (2-dimensional sphere), in more detail. Then we will construct the inverse Gabor transformation explicitly.","PeriodicalId":439086,"journal":{"name":"2014 International Conference on Wavelet Analysis and Pattern Recognition","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Gabor transformation on the circle\",\"authors\":\"K. Fujita\",\"doi\":\"10.1109/ICWAPR.2014.6961302\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In [2] and [3], we considered the Gabor transform of analytic functionals on the sphere in general dimension and we expressed it by a series expansion with the spherical harmonics and the Bessel functions. In this paper, following our previous results, we will consider the Gabor transform of analytic functionals, especially of square integrable functions on the circle (2-dimensional sphere), in more detail. Then we will construct the inverse Gabor transformation explicitly.\",\"PeriodicalId\":439086,\"journal\":{\"name\":\"2014 International Conference on Wavelet Analysis and Pattern Recognition\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-07-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2014 International Conference on Wavelet Analysis and Pattern Recognition\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICWAPR.2014.6961302\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2014 International Conference on Wavelet Analysis and Pattern Recognition","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICWAPR.2014.6961302","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In [2] and [3], we considered the Gabor transform of analytic functionals on the sphere in general dimension and we expressed it by a series expansion with the spherical harmonics and the Bessel functions. In this paper, following our previous results, we will consider the Gabor transform of analytic functionals, especially of square integrable functions on the circle (2-dimensional sphere), in more detail. Then we will construct the inverse Gabor transformation explicitly.
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