{"title":"具有变阶导数的hermite - fejsamir插值算子的范数","authors":"Alexander Fedotov","doi":"10.59400/jam.v2i1.87","DOIUrl":null,"url":null,"abstract":"A new definition of a variable order derivative is given. It is based on interpolation of integer order differentiation operators. An interpolation operator of the Hermite-Fejér type is built to jointly interpolate the function and its derivative of variable order. The upper estimate of the norm of this operator is obtained. This norm has been shown to be limited.","PeriodicalId":495855,"journal":{"name":"Journal of AppliedMath","volume":"21 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Norm of the Hermite-Fejér interpolative operator with derivatives of variable order\",\"authors\":\"Alexander Fedotov\",\"doi\":\"10.59400/jam.v2i1.87\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A new definition of a variable order derivative is given. It is based on interpolation of integer order differentiation operators. An interpolation operator of the Hermite-Fejér type is built to jointly interpolate the function and its derivative of variable order. The upper estimate of the norm of this operator is obtained. This norm has been shown to be limited.\",\"PeriodicalId\":495855,\"journal\":{\"name\":\"Journal of AppliedMath\",\"volume\":\"21 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of AppliedMath\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.59400/jam.v2i1.87\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of AppliedMath","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.59400/jam.v2i1.87","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Norm of the Hermite-Fejér interpolative operator with derivatives of variable order
A new definition of a variable order derivative is given. It is based on interpolation of integer order differentiation operators. An interpolation operator of the Hermite-Fejér type is built to jointly interpolate the function and its derivative of variable order. The upper estimate of the norm of this operator is obtained. This norm has been shown to be limited.
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