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

Pub Date : 2024-03-15 DOI:10.1007/s11868-024-00596-0
Ajay K. Gupt, Akhilesh Prasad
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引用次数: 0

摘要

本文介绍了与列别杰夫-斯卡尔斯卡娅变换有关的无穷阶积分微分算子。我们得到了该算子的一些特征。此外,我们建立了一类无穷阶积分微分算子在 \( L^2({\mathbb {R}}_{+}; \, dx)\)上单元化的必要条件和充分条件。最后还研究了一些相关的整微分方程类。
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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.

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