20 citations · 46 across the 15 of their papers we have counts for
20 papers
On the measure of spectra for discrete Schrödinger operators on periodic graphs
Natalia Saburova
We consider discrete Schrödinger operators with real periodic potentials on periodic graphs, where is the adjacency operator and is a coupling…
Spectral invariants for discrete Schrödinger operators on periodic graphs
Natalia Saburova
The aim of this article is to present a complete system of Floquet spectral invariants for the discrete Schrödinger operators with periodic potentials on periodic graphs. These inv…
Spectrum of Schrödinger operators on subcovering graphs
Natalia Saburova
We consider discrete Schrödinger operators with real periodic potentials on periodic graphs. The spectra of the operators consist of a finite number of bands. By "rolling up" a per…
Asymptotic isospectrality of Schrödinger operators on periodic graphs
Natalia Saburova
We consider discrete Schrödinger operators with periodic potentials on periodic graphs. Their spectra consist of a finite number of bands. We perturb a periodic graph by adding edg…
Trace formulas for magnetic Schrödinger operators on periodic graphs and their applications
Evgeny Korotyaev, Natalia Saburova
We consider Schrödinger operators with periodic magnetic and electric potentials on periodic discrete graphs. The spectrum of such operators consists of a finite number of bands. W…
Two-sided estimates of total bandwidth for Schrödinger operators on periodic graphs
Evgeny Korotyaev, Natalia Saburova
We consider Schrödinger operators with periodic potentials on periodic discrete graphs. Their spectrum consists of a finite number of bands. We obtain two-sided estimates of the to…
On continuous spectrum of magnetic Schrödinger operators on periodic discrete graphs
Evgeny Korotyaev, Natalia Saburova
We consider Schrödinger operators with periodic electric and magnetic potentials on periodic discrete graphs. The spectrum of such operators consists of an absolutely continuous (a…
Invariants of magnetic Laplacians on periodic graphs
Evgeny Korotyaev, Natalia Saburova
We consider a magnetic Laplacian with periodic magnetic potentials on periodic discrete graphs. Its spectrum consists of a finite number of bands, where degenerate bands are eigenv…
Invariants for Laplacians on periodic graphs
E. Korotyaev, N. Saburova
We consider a Laplacian on periodic discrete graphs. Its spectrum consists of a finite number of bands. In a class of periodic 1-forms, i.e., functions defined on edges of the peri…
Spectral estimates for Schrödinger operators on periodic discrete graphs
E. Korotyaev, N. Saburova
We consider normalized Laplacians and their perturbations by periodic potentials (Schrödinger operators) on periodic discrete graphs. The spectrum of the operators consists of an a…
Laplacians on periodic graphs with guides
Evgeny Korotyaev, Natalia Saburova
We consider Laplace operators on periodic discrete graphs perturbed by guides, i.e., graphs which are periodic in some directions and finite in other ones. The spectrum of the Lapl…
Schrödinger operators with guided potentials on periodic graphs
Evgeny Korotyaev, Natalia Saburova
We consider discrete Schrödinger operators with periodic potentials on periodic graphs perturbed by guided non-positive potentials, which are periodic in some directions and finite…
Magnetic Schrödinger operators on periodic discrete graphs
Evgeny Korotyaev, Natalia Saburova
We consider magnetic Schrödinger operators with periodic magnetic and electric potentials on periodic discrete graphs. The spectrum of the operators consists of an absolutely conti…
Scattering on periodic metric graphs
Evgeny Korotyaev, Natalia Saburova
We consider the Laplacian on a periodic metric graph and obtain its decomposition into a direct fiber integral in terms of the corresponding discrete Laplacian. Eigenfunctions and…
Effective masses for Laplacians on periodic graphs
Evgeny Korotyaev, Natalia Saburova
We consider Laplacians on periodic both discrete and metric equilateral graphs. Their spectrum consists of an absolutely continuous part (which is a union of non-degenerate spectra…
Spectral band bracketing for Laplacians on periodic metric graphs
Evgeny Korotyaev, Natalia Saburova
We consider Laplacians on periodic metric graphs with unit-length edges. The spectrum of these operators consists of an absolutely continuous part (which is a union of an infinite…
Estimates of bands for Laplacians on periodic equilateral metric graphs
Evgeny Korotyaev, Natalia Saburova
We consider Laplacians on periodic equilateral metric graphs. The spectrum of the Laplacian consists of an absolutely continuous part (which is a union of an infinite number of non…
Spectral band localization for Schrödinger operators on periodic graphs
Evgeny Korotyaev, Natalia Saburova
We consider Schrödinger operators on periodic discrete graphs. It is known that the spectrum of these operators has band structure. We obtain a localization of spectral bands in te…
Schrödinger operators on periodic discrete graphs
Evgeny Korotyaev, Natalia Saburova
We consider Schrödinger operators with periodic potentials on periodic discrete graphs. The spectrum of the Schrödinger operator consists of an absolutely continuous part (a union…
Laplacians on periodic discrete graphs
Andrey Badanin, Evgeny Korotyaev, Natalia Saburova
We consider Laplacians on -periodic discrete graphs. The following results are obtained: 1) The Floquet-Bloch decomposition is constructed and basic properties are derived. 2…