Abstract
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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This work is supported by the Council of Scientific and Industrial Research (CSIR), India, under file no. 09/085(0123)/2019-EMR-I.
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Both authors have equally contributed to writing and preparing the manuscript text. AKG contributed to the investigation, conceptualization, methodology, and the original draft of the writing. AP provided supervision, validation and contributed to the investigation and methodology.
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Gupt, A.K., Prasad, A. The infinite-order integro-differential operator related to the Lebedev–Skalskaya transform. J. Pseudo-Differ. Oper. Appl. 15, 21 (2024). https://doi.org/10.1007/s11868-024-00596-0
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DOI: https://doi.org/10.1007/s11868-024-00596-0