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Lebedev–Skalskaya transforms and allied operators on certain function spaces
Integral Transforms and Special Functions ( IF 0.7 ) Pub Date : 2021-06-14 , DOI: 10.1080/10652469.2021.1935922
U. K. Mandal 1 , Akhilesh Prasad 2
Affiliation  

In this paper, some elementary and useful terminologies associated to Lebedev–Skalskaya transform (LS-transform) are notified and then estimates for Rκ12+iτ(x), Fκ12+iτ(x), translation and convolution operators associated to LS-transform are obtained. The continuity of LS-transforms, translation and convolution operators on functions spaces Sα,k, Hα,k and Gα,k are discussed. The continuity of pseudo-differential operators in terms of LS-transforms is discussed on functions spaces Sα,k, Hα,k, Gα,k and Lebesgue space. At the end, an application of LS-transform is shown by solving a differential equation of convolution type.



中文翻译:

Lebedev-Skalskaya 变换和某些函数空间上的联合算子

在本文中,通知了与 Lebedev-Skalskaya 变换 (LS-transform) 相关的一些基本且有用的术语,然后估计Rκ12+一世τ(X),Fκ12+一世τ(X),获得与LS变换相关的平移和卷积算子。函数空间上 LS 变换、平移和卷积算子的连续性小号α,ķ,Hα,ķGα,ķ被讨论。在函数空间上讨论了伪微分算子在 LS 变换方面的连续性小号α,ķ,Hα,ķ,Gα,ķ和勒贝格空间。最后,通过求解卷积类型的微分方程展示了LS变换的应用。

更新日期:2021-06-14
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