3 citations · 5 across the 7 of their papers we have counts for
7 papers
Weil-Titchmarsh theory as applied to the singular non-sectorial Schrödinger operator. Conditions for discreteness of the spectrum and compactness of the resolvent
Sergey N. Tumanov
The spectral properties of the singular Schrödinger operator with complex-valued potential which takes values in a wider region than the half-plane, have been little studied. In ge…
The Complex Airy Operator as Explicitly Solvable PT-symmetrical Model
A. A. Shkalikov, S. N. Tumanov
We study the Sturm--Liouville operator with concrete -- symmetric potential and Dirichlet boundary…
Completeness theorem for the system of eigenfunctions of the complex Schrödinger operator
Sergey Tumanov
The completeness of the system of eigenfunctions of the complex Schrödinger operator on the semi-axis with Dirichlet boundary conditions is proved fo…
Completeness theorem for the system of eigenfunctions of the complex Schrödinger operator
Sergey Tumanov
We prove the completeness of the system of eigenfunctions of the complex Schrödinger operator on the semiaxis in with Dirichlet boundary con…
Eigenvalue Dynamics of a PT-symmetric Sturm-Liouville Operator. Criteria of the Similarity to a Self-adjoint or Normal Operator
A. A. Shkalikov, S. N. Tumanov
The goal of the paper is to investigate the dynamics of the eigenvalues of the Sturm-Liouville operator with summable PT-symmetric potential on the finite interval. It turns out th…
The Limit Spectral Graph in the Semi-Classical Approximation for the Sturm-Liouville Problem With a Complex Polynomial Potential
A. A. Shkalikov, S. N. Tumanov
The limit distribution of the discrete spectrum of the Sturm-Liouville problem with complex-valued polynomial potential on an interval, on a half-axis, and on the entire axis is st…