52 citations · 786 across the 59 of their papers we have counts for
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A Neumann series of Bessel functions representation for solutions of the radial Dirac system
Vladislav V. Kravchenko, Elina L. Shishkina, Sergii M. Torba
A new representation for a regular solution of the radial Dirac system of a special form is obtained. The solution is represented as a Neumann series of Bessel functions uniformly…
A transmutation operator method for solving the inverse quantum scattering problem
Vladislav V. Kravchenko, Elina L. Shishkina, Sergii M. Torba
The inverse quantum scattering problem for the perturbed Bessel equation is considered. A direct and practical method for solving the problem is proposed. It allows one to reduce t…
A right inverse operator for and applications
Briceyda B. Delgado, Vladislav V. Kravchenko
A general solution of the equation is obtained for an arbitrary bounded domain $Ω\subset\mathbb{…
Construction of a transmutation for the one-dimensional Schrödinger operator and a representation for solutions
Vladislav V. Kravchenko
A new representation for solutions of the one-dimensional Schrödinger equation -u"+q(x)u=w^2u is obtained in the form of a series possessing the following attractive feature. The t…
Transmutations and spectral parameter power series in eigenvalue problems
Vladislav V. Kravchenko, Sergii M. Torba
We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS). The possibil…
Transmutations for Darboux transformed operators with applications
Vladislav V. Kravchenko, Sergii M. Torba
We solve the following problem. Given a continuous complex-valued potential q_1 defined on a segment [-a,a] and let q_2 be the potential of a Darboux transformed Schrödinger operat…