2 citations · 2 across the 5 of their papers we have counts for
5 papers · 1 filter
On the generalized Lebedev index transform
Semyon Yakubovich
An essential generalization of the Lebedev index transform with the square of the Macdonald function is investigated. Namely, we consider a family of integral operators with the po…
The Kontorovich-Lebedev transform as a map between -orthogonal polynomials
Ana F. Loureiro, S. Yakubovich
A slight modification of the Kontorovich-Lebedev transform is an automorphism on the vector space of polynomials. The action of this -transform over certain polynomial sequen…
On an inequality for the Riemann zeta-function in the critical strip
Sadegh Nazardonyavi, Semyon Yakubovich
By using new power inequalities we give an elementary proof of an important relation for the Riemann zeta-function |ζ(1-s)| <= |ζ(s)| in the strip 0< Re s<1/2,\ |\Im s| >= 12. More…
A new Kontorovich-Lebedev-like transformation
Semyon Yakubovich
A different application of the familiar integral representation for the modifed Bessel function drives to a new Kontorovich-Lebedev-like integral transformation of a general comple…
Integral and series transformations via Ramanujan's identities and Salem's type equivalences to the Riemann hypothesis
Semyon Yakubovich
We consider integral and series transformations, which are associated with Ramanujan's identities, involving various arithmetic functions and a ratio of products of Riemann's zeta…