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.

中文翻译：

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与 Lebedev-Skalskaya 变换相关的无限阶积分微分算子

在本文中，我们介绍与 Lebedev-Skalskaya 变换相关的无限阶积分微分算子。获得了该算子的一些特征。此外，我们建立了一类无限阶积分微分算子在\( L^2({\mathbb {R}}_{+}; \, dx)\) 上酉的充要条件。最后还研究了一些相关的积分微分方程。