A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger operators.
A new approach to inverse spectral theory. II: General real potentials and the connection to the spectral measure.
A note on a linear spectral theorem for a class of first order systems in .
A trace formula of a boundary value problem for the operator Sturm-Liouville equation.
An abstract approach to some spectral problems of direct sum differential operators.
An inverse problem for Sturm-Liouville operators on the half-line having Bessel-type singularity in an interior point
We study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided, also necessary and sufficient conditions for the solvability of the inverse problem are obtained.
Analysis and comparison of several components mode synthesis methods on one-dimensional domains.
Asymptotic analysis of non-self-adjoint Hill operators
We obtain uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L t (q) with a potential q ∈ L 1[0,1] and t-periodic boundary conditions, t ∈ (−π, π]. Using these formulas, we find sufficient conditions on the potential q such that the number of spectral singularities in the spectrum of the Hill operator L(q) in L 2(−∞,∞) is finite. Then we prove that the operator L(q) has no spectral singularities at infinity and it is an asymptotically spectral operator...