{"title":"关于贝塞尔--里兹算子","authors":"R. A. Cerutti","doi":"10.30972/fac.2306816","DOIUrl":null,"url":null,"abstract":"We consider a class of conv olution operator denoted ϕα W obtained by convolution with a generalized function expressible in terms of the Bessel function on first kind γ J with argument the distribution ( ) P ± i0 . We study some elementary properties of the operator ϕα W like the semigroup property ϕ = ϕ α β α+β W W W ; and ( +m2 ) α α−2 W ϕ = W for α > 2 where ( +m2 ) is the Klein-Gordon ultrahyperbolic operator. Moreover we prove that the operator ϕα W may be consider as a negative power of the Klein-Gordon operato","PeriodicalId":502481,"journal":{"name":"FACENA","volume":"41 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON BESSEL-RIESZ OPERATORS\",\"authors\":\"R. A. Cerutti\",\"doi\":\"10.30972/fac.2306816\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a class of conv olution operator denoted ϕα W obtained by convolution with a generalized function expressible in terms of the Bessel function on first kind γ J with argument the distribution ( ) P ± i0 . We study some elementary properties of the operator ϕα W like the semigroup property ϕ = ϕ α β α+β W W W ; and ( +m2 ) α α−2 W ϕ = W for α > 2 where ( +m2 ) is the Klein-Gordon ultrahyperbolic operator. Moreover we prove that the operator ϕα W may be consider as a negative power of the Klein-Gordon operato\",\"PeriodicalId\":502481,\"journal\":{\"name\":\"FACENA\",\"volume\":\"41 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-08-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"FACENA\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30972/fac.2306816\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"FACENA","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30972/fac.2306816","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们考虑的是一类卷积算子，记为ϕα W，它是通过与参数为分布 ( ) P ± i0 的第一类贝塞尔函数 γ J 的广义函数卷积而得到的。我们研究了算子 ϕα W 的一些基本性质，如半群性质 ϕ = ϕα β α+β W W ；以及 α > 2 时 ( +m2 ) α α-2 W ϕ = W，其中 ( +m2 ) 是克莱因-戈登超双曲算子。此外，我们还证明，可以把算子 ϕα W 视为克莱因-戈登算子的负幂。
We consider a class of conv olution operator denoted ϕα W obtained by convolution with a generalized function expressible in terms of the Bessel function on first kind γ J with argument the distribution ( ) P ± i0 . We study some elementary properties of the operator ϕα W like the semigroup property ϕ = ϕ α β α+β W W W ; and ( +m2 ) α α−2 W ϕ = W for α > 2 where ( +m2 ) is the Klein-Gordon ultrahyperbolic operator. Moreover we prove that the operator ϕα W may be consider as a negative power of the Klein-Gordon operato
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