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arXiv · 2607.22343

The fractional Kontorovich-Lebedev transform

Semyon Yakubovich
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Abstract

We introduce the so-called fractional analog of the Kontorovich-Lebedev transform, modifying its kernel, which is the Macdonald function $K_\nu(z)$. Properties of this kernel as well as mapping properties of the new index transform are investigated. The inversion formula in suitable spaces of functions is established.

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Semyon Yakubovich. 2026-07-24. The fractional Kontorovich-Lebedev transform. https://arxiv.org/abs/2607.22343

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