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...
Banded matrices and discrete Sturm-Liouville eigenvalue problems.
Bergman spaces on some tube-type domains and Laguerre operators on symmetric cones.
Bispectral commutative ordinary differential operators.
Calogero-Moser spaces and an adelic -algebra
We introduce a Lie algebra, which we call adelic -algebra. Then we construct a natural bosonic representation and show that the points of the Calogero-Moser spaces are in 1:1 correspondence with the tau-functions in this representation.
Characterizing degenerate Sturm-Liouville problems.
Computing eigenvalues of regular Sturm-Liouville problems.
Discrete spectrum and principal functions of non-selfadjoint differential operator
In this article, we consider the operator defined by the differential expression in , where is a complex valued function. Discussing the spectrum, we prove that has a finite number of eigenvalues and spectral singularities, if the condition holds. Later we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities.
Eigenvalue characterization for a class of boundary value problems.
Eigenvalue computations for regular matrix Sturm-Liouville problems.
Eigenvalue problems for -Laplacian functional dynamic equations on time scales.
Eigenvalue problems for systems of nonlinear boundary value problems on time scales.
Essential self-adjointness of symmetric linear relations associated to first order systems
The purpose of this note is to present several criteria for essential self-adjointness. The method is based on ideas due to Shubin. This note is divided into two parts. The first part deals with symmetric first order systems on the line in the most general setting. Such a symmetric first order system of differential equations gives rise naturally to a symmetric linear relation in a Hilbert space. In this case even regularity is nontrivial. We will announce a regularity result and discuss criteria...