arXiv subjects

Alexander Kiselev

Publications and source records attributed to Alexander Kiselev.

75 records · Page 5Linked to original sources

arXiv1997

Absolutely continuous spectrum of perturbed Stark operators

We prove new results on the stability of the absolutely continuous spectrum for perturbed Stark operators with decaying or satisfying certain smoothness assumption perturbation. We show that the absolutely continuous spectrum of the Stark operator is stable if the perturbing potential decays at the rate $(1+x)^{-\frac{1}{3}-ε}$ or if it is continuously differentiable with derivative from the Hölder space $C_α(R),$ with any $α>0.$

math.SP↗

arXiv1996

Preservation of the absolutely continuous spectrum of Schrödinger equation under perturbations by slowly decreasing potentials and a.e. convergence of integral operators

We prove new criteria of stability of the absolutely continuous spectrum of one-dimensional Schrödinger operators under slowly decaying perturbations. As applications, we show that the absolutely continuous spectrum of the free and periodic Schrödinger operators is preserved under perturbations by all potentials $V(x)$ satisfying $|V(x)| \leq C(1+x)^{-\frac{2}{3}-ε}.$ The main new technique includes an a.e.\ convergence theorem for a class of integral operators.

math.SP↗

arXiv1996

An interpolation theorem related to the a.e. convergence of integral operators

We show that for integral operators of general form the norm bounds in Lorentz spaces imply certain norm bounds for the maximal function. As a consequence, the a.e. convergence for the integral operators on the Lorentz spaces follows from the appropriate norm estimates.

math.CA↗