We review recent developments in the theory of 1-D Schrödinger operators with local point
interactions on a discrete set. The progress in this area was stimulated by recent advances …

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 …

The spectral properties of Dirac operators on $(0, 1) $ with potentials that belong entrywise
to $ L_p (0, 1) $, for some $ p\in [1,\infty) $, are studied. The algorithm of reconstruction of the …

We solve the inverse spectral problem for a class of Sturm–Liouville operators with singular
non-local potentials and non-local boundary conditions. We study to what extent the …

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 investigate the eigenvalues of perturbed spherical Schrödinger operators under the
assumption that the perturbation q (x) satisfies xq (x)∊ L 1 (0, 1). We show that the square …

Ly=− y+ q (x) y, x∈[0, π],(0.1) на конечном интервале. Первая задача связана с
восстановлением потенциала по двум спектрам этого оператора, порожденного …

We explore the connections between singular Weyl–Titchmarsh theory and the single and
double commutation methods. In particular, we compute the singular Weyl function of the …

Continuous Analogs of Polynomials Orthogonal on the Unit Circle and Krein Systems Page 1
IMRS International Mathematics Research Surveys Volume 2006, Article ID 54517, Pages …

We discuss inverse spectral theory for singular differential operators on arbitrary intervals
$(a, b)\subseteq\mathbb {R} $ associated with rather general differential expressions of the …