论文标题
离散的Lebedev-Skalskaya变换
Discrete Lebedev-Skalskaya transforms
论文作者
论文摘要
引入和研究了LeBedev-Skalskaya变换的离散类似物。它涉及系列和积分相对于内核$ {\ rm re} k_ {α+in}（x），{\ rm im} k_ {α{α+in}（x），x> 0，n \ in \ mathbb {n} <1，\ i $是虚构的单位，$k_ν（z）$是修改的贝塞尔功能。当$α= \ pm 1/2 $时，建立了适用于这些系列和积分的合适函数和序列的相应反转公式。 $α= 0 $的情况减少到Kontorovich-Lebedev变换。
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.
