121 citations · 392 across the 18 of their papers we have counts for
14 papers · 1 filter
Inverse scattering for reflectionless Schrödinger operators with integrable potentials and generalized soliton solutions for the KdV equation
Rostyslav Hryniv, Bohdan Melnyk, Yaroslav Mykytyuk
We give a complete characterisation of the reflectionless Schrödinger operators on the line with integrable potentials, solve the inverse scattering problem of reconstructing such…
On the First Trace Formula for Schrödinger Operators
Rostyslav Hryniv, Yaroslav Mykytyuk
We prove that the so-called first trace formula holds for all Schrödinger operators on the line with real-valued integrable potentials.
Bari-Markus property for Dirac operators
Ya. V. Mykytyuk, D. V. Puyda
We prove the Bari-Markus property for spectral projectors of non-self-adjoint Dirac operators on a finite interval with square-integrable matrix-valued potentials and some separate…
On the accelerants of non-self-adjoint Dirac operators
Ya. V. Mykytyuk, D. V. Puyda
We prove that there is a homeomorphism between the space of accelerants and the space of potentials of non-self-adjoint Dirac operators on a finite interval.
Self-adjointness of Schroedinger operators with singular potentials
Rostyslav O. Hryniv, Yaroslav V. Mykytyuk
We study one-dimensional Schroedinger operators S with real-valued distributional potentials q in W^{-1}_{2,loc}(R) and prove an extension of the Povzner-Wienholtz theorem on self-…
Inverse scattering on the line for Schrödinger operators with Miura potentials, II. Different Riccati representatives
R. O. Hryniv, Ya. V. Mykytyuk, P. A. Perry
This is the second in a series of papers on scattering theory for one-dimensional Schrödinger operators with Miura potentials admitting a Riccati representation of the form $q=u'+u…