Spectral properties of 1-D Schrödinger operators [Formula: see text] with local point
interactions on a discrete set [Formula: see text] are well studied when d∗:= infn, k∈ N| xn …

We systematically develop Weyl-Titchmarsh theory for singular differential operators on
arbitrary intervals $(a, b)\subseteq\mathbb {R} $ associated with rather general differential …

We study the system of root functions (SRF) of Hill operator Ly=− y ″+ vy with a singular
(complex-valued) potential v∈ Hper− 1 and the SRF of 1D Dirac operator Ly= i (100− 1) …

We consider magnetic Schrödinger operators on quantum graphs with identical edges. The
spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the …

Two inverse problems for the Sturm-Liouville operator Ly= sy ″+ q (x) y on the interval [0, fy]
are studied. For θ⩾ 0, there is a mapping F: W 2 θ→ l B θ, F (σ)={sk} 1∞, related to the first of …

We construct transformation operators for Sturm-Liouville operators with singular potentials
from the space W− 1 2 (0, 1) and show that these transformation operators naturally appear …

We study the Hamiltonians HX, α, q with δ-type point interactions at the centers xk on the
positive half line in terms of energy forms. We establish analogs of some classical results on …

We study the inverse spectral problem of reconstructing energy-dependent Sturm–Liouville
equations from their Dirichlet spectra and sequences of the norming constants. For the class …

We study the asymptotic behavior of the eigenvalues the Sturm-Liouville operator Ly=− y ″+
q (x) y with potentials from the Sobolev space W 2 θ− 1, θ≥ 0, including the nonclassical …

We turn back to the well known problem of interpretation of the Schrodinger operator with
the pseudopotential being the first derivative of the Dirac function. We show that the problem …