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arXiv · 2008.13263

Discrete Lebedev-Skalskaya transforms

Semyon Yakubovich
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Abstract

Discrete analogs of the Lebedev-Skalskaya transforms are introduced and investigated. It involves series and integrals with respect to the kernels ${\rm Re} K_{α+in}(x), {\rm Im} K_{α+in}(x), x >0, n \in \mathbb{N}, |α| < 1,\ i $ is the imaginary unit and $K_ν(z)$ is the modified Bessel function. The corresponding inversion formulas for suitable functions and sequences in terms of these series and integrals are established when $α= \pm 1/2$. The case $α=0$ reduces to the Kontorovich-Lebedev transform.

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Semyon Yakubovich. 2020-08-30. Discrete Lebedev-Skalskaya transforms. https://arxiv.org/abs/2008.13263

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