6 papers · 1 filter
Resonances sets of Schrödinger operators
Yurii Belov, Pavel Gubkin
We prove that resonances of the Schrödinger operator with compactly supported potential can contain arbitrary subset of the angle that satis…
Direct and inverse spectral continuity for Dirac operators
Roman Bessonov, Pavel Gubkin
The half-line Dirac operators with -potentials can be characterized by their spectral data. It is known that the spectral correspondence is a homeomorphism: close potentials g…
Krein systems with oscillating potentials
Pavel Gubkin
We prove that mean decay of the coefficient of Krein system is equivalent to the mean decay of the Fourier transform of its Szegő function.
Stability of Schur's iterates and fast solution of the discrete integrable NLS
R. V. Bessonov, P. V. Gubkin
We prove a sharp stability estimate for Schur iterates of contractive analytic functions in the open unit disk. We then apply this result in the setting of the inverse scattering a…
Dirac operators with exponentially decaying entropy
Pavel Gubkin
We prove that the Weyl function of the one-dimensional Dirac operator on the half-line with exponentially decaying entropy extends meromorphically into the horizonta…
Mate-Nevai-Totik theorem for Krein systems
Pavel Gubkin
We prove the Cesàro boundedness of eigenfunctions of the Dirac operator on the half-line with a square-summable potential. The proof is based on the theory of Krein systems and, in…