The fractional Kontorovich-Lebedev transform

2026/07/24 by Semyon Yakubovich
Mathematics · #math.CA

paper · pdf

Abstract

We introduce the so-called fractional analog of the Kontorovich-Lebedev transform, modifying its kernel, which is the Macdonald function K_ν(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.

Related

• On the generalized Lebedev index transform
• Discrete Kontorovich-Lebedev transforms
• Discrete Lebedev-Skalskaya transforms
• A class of index transforms generated by the Mellin and Laplace\n operators
• Uniform upper bounds and asymptotic expansions for certain index kernels