5 papers
Discrete Lebedev-Skalskaya transforms
Semyon Yakubovich
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…
Discrete Mehler-Fock transforms
Semyon Yakubovich
Discrete analogs of the classical Mehler-Fock transforms are introduced and investigated. It involves series with the associated Legendre function $P^μ_{in-1/2}(x), x > 1,\ {\rm Re…
Index transforms with the product of the associated Legendre functions
Semyon Yakubovich
Index transforms with the product of the associated Legendre functions are introduced. Mapping properties are investigated in the Lebesgue spaces. Inversion formulas are proved. Th…
Index transforms with the squares of Kelvin functions
Semyon Yakubovich
New index transforms, involving squares of Kelvin functions, are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. Th…
Index transforms with Weber type kernels
Semyon Yakubovich
New index transforms with Weber type kernels, consisting of products of Bessel functions of the first and second kind are investigated. Mapping properties and inversion formulas ar…