52 citations · 535 across the 39 of their papers we have counts for
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math.CA2017
On construction of transmutation operators for perturbed Bessel equations
Vladislav V. Kravchenko, Elina L. Shishkina, Sergii M. Torba
A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with co…
math.CA2017★ 3 cited
Transmutation operators: construction and applications
Vladislav V. Kravchenko, Sergii M. Torba, Kira V. Khmelnytskaya
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Sc…
math.CA2017★ 7 cited
Asymptotics with respect to the spectral parameter and Neumann series of Bessel functions for solutions of the one-dimensional Schrödinger equation
Vladislav V. Kravchenko, Sergii M. Torba
A representation for a solution of the equation , satisfying the initial conditions , is derived in the form \[ u(ω,x)=e^{iωx}\left…