{"title":"积分变换","authors":"Massoud Malek","doi":"10.1002/9781119423461.ch2","DOIUrl":null,"url":null,"abstract":"A function F (u) defined in this way ( t may be either a real or a complex variable) is called an integral transform of f (t) . The function K(t , u) which appears in the integrand is referred to as the kernel of the transform. There are numerous useful integral transforms. Each is specified by the kernel K (t , u) . Some kernels have an associated inverse kernel K −1 (t , u) which (roughly speaking) yields an inverse transform: f (t) = ∫ u2","PeriodicalId":366025,"journal":{"name":"Advanced Numerical and Semi-Analytical Methods for Differential Equations","volume":"30 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Integral Transforms\",\"authors\":\"Massoud Malek\",\"doi\":\"10.1002/9781119423461.ch2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A function F (u) defined in this way ( t may be either a real or a complex variable) is called an integral transform of f (t) . The function K(t , u) which appears in the integrand is referred to as the kernel of the transform. There are numerous useful integral transforms. Each is specified by the kernel K (t , u) . Some kernels have an associated inverse kernel K −1 (t , u) which (roughly speaking) yields an inverse transform: f (t) = ∫ u2\",\"PeriodicalId\":366025,\"journal\":{\"name\":\"Advanced Numerical and Semi-Analytical Methods for Differential Equations\",\"volume\":\"30 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-04-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advanced Numerical and Semi-Analytical Methods for Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/9781119423461.ch2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advanced Numerical and Semi-Analytical Methods for Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/9781119423461.ch2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A function F (u) defined in this way ( t may be either a real or a complex variable) is called an integral transform of f (t) . The function K(t , u) which appears in the integrand is referred to as the kernel of the transform. There are numerous useful integral transforms. Each is specified by the kernel K (t , u) . Some kernels have an associated inverse kernel K −1 (t , u) which (roughly speaking) yields an inverse transform: f (t) = ∫ u2
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