Asymptotics for eigenvalues of Schrödinger operator with small shift and Dirichlet condition

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Abstract

We consider a non-self-adjoint Schrödinger operator on the unit segment with the Dirichlet condition perturbed by an operator of small translation. The main result is the three-terms asymptotics for the eigenvalues with respect to their index and this asymptotics is uniform in the small translation. We also show that the system of eigenfunctions and associated functions of the considered operators forms a Bari basis in the space of functions square integrable on the considered unit segment.

About the authors

D. I. Borisov

Institute of Mathematics, Ufa Federal Research Center, Russian Academy of Sciences

Author for correspondence.
Email: borisovdi@yandex.ru
Russian Federation, Ufa

D. M. Polyakov

Institute of Mathematics, Ufa Federal Research Center, Russian Academy of Sciences; Southern Mathematical Institute, Vladikavkaz Scientific Center, Russian Academy of Sciences

Email: DmitryPolyakow@mail.ru
Russian Federation, Ufa; Vladikavkaz

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