{"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}
引用次数: 0
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
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