{"title":"与列别杰夫-斯卡尔斯卡娅变换有关的无穷阶积分微分算子","authors":"Ajay K. Gupt, Akhilesh Prasad","doi":"10.1007/s11868-024-00596-0","DOIUrl":null,"url":null,"abstract":"<p>In this article, we introduce infinite-order integro-differential operator related to Lebedev–Skalskaya transform. Some characteristics of this operator are obtained. Furthermore, we establish the necessary and sufficient conditions for a class of infinite-order integro-differential operators to be unitary on <span>\\( L^2({\\mathbb {R}}_{+}; \\, dx)\\)</span>. Some classes of related integro-differential equations are also studied at the end.\n</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The infinite-order integro-differential operator related to the Lebedev–Skalskaya transform\",\"authors\":\"Ajay K. Gupt, Akhilesh Prasad\",\"doi\":\"10.1007/s11868-024-00596-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this article, we introduce infinite-order integro-differential operator related to Lebedev–Skalskaya transform. Some characteristics of this operator are obtained. Furthermore, we establish the necessary and sufficient conditions for a class of infinite-order integro-differential operators to be unitary on <span>\\\\( L^2({\\\\mathbb {R}}_{+}; \\\\, dx)\\\\)</span>. Some classes of related integro-differential equations are also studied at the end.\\n</p>\",\"PeriodicalId\":48793,\"journal\":{\"name\":\"Journal of Pseudo-Differential Operators and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Pseudo-Differential Operators and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11868-024-00596-0\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pseudo-Differential Operators and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11868-024-00596-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
The infinite-order integro-differential operator related to the Lebedev–Skalskaya transform
In this article, we introduce infinite-order integro-differential operator related to Lebedev–Skalskaya transform. Some characteristics of this operator are obtained. Furthermore, we establish the necessary and sufficient conditions for a class of infinite-order integro-differential operators to be unitary on \( L^2({\mathbb {R}}_{+}; \, dx)\). Some classes of related integro-differential equations are also studied at the end.
期刊介绍:
The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.