Zobrazeno 1 - 10
of 17
pro vyhledávání: '"47A10, 05C63"'
Autor:
Saburova, Natalia
We consider discrete Schr\"odinger operators with periodic potentials on periodic graphs. Their spectra consist of a finite number of bands. By "rolling up" a periodic graph along some appropriate directions we obtain periodic graphs of smaller dimen
Externí odkaz:
http://arxiv.org/abs/2409.05830
Autor:
Saburova, Natalia
We consider discrete Schr\"odinger operators with periodic potentials on periodic graphs. Their spectra consist of a finite number of bands. We perturb a periodic graph by adding edges in a periodic way (without changing the vertex set) and show that
Externí odkaz:
http://arxiv.org/abs/2402.10780
Autor:
Korotyaev, Evgeny, Saburova, Natalia
We consider Schr\"odinger operators with periodic magnetic and electric potentials on periodic discrete graphs. The spectrum of such operators consists of a finite number of bands. We determine trace formulas for the magnetic Schr\"odinger operators.
Externí odkaz:
http://arxiv.org/abs/2206.09663
Autor:
Korotyaev, Evgeny, Saburova, Natalia
We consider Schr\"odinger operators with periodic potentials on periodic discrete graphs. Their spectrum consists of a finite number of bands. We obtain two-sided estimates of the total bandwidth for the Schr\"odinger operators in terms of geometric
Externí odkaz:
http://arxiv.org/abs/2106.08661
We study the spectrum of the Laplacian on the Sierpinski lattices. First, we show that the spectrum of the Laplacian, as a subset of $\mathbb{C}$, remains the same for any $\ell^p$ spaces. Second, we characterize all the spectral points for the latti
Externí odkaz:
http://arxiv.org/abs/1910.01771
Publikováno v:
Linear Algebra and its Applications 547 (2018) 183-216
The aim of this article is to give a simple geometric condition that guarantees the existence of spectral gaps of the discrete Laplacian on periodic graphs. For proving this, we analyse the discrete magnetic Laplacian (DML) on the finite quotient and
Externí odkaz:
http://arxiv.org/abs/1710.01157
Autor:
Parra, Daniel, Richard, Serge
Publikováno v:
Rev. Math. Phys. 30 (2018), no. 4, 1850009, 39 pp
In this paper we investigate the spectral and the scattering theory of Schr\"odinger operators acting on perturbed periodic discrete graphs. The perturbations considered are of two types: either a multiplication operator by a short-range or a long-ra
Externí odkaz:
http://arxiv.org/abs/1607.03573
Publikováno v:
Journal of Fourier Analysis and Applications. 27
We study the spectrum of the Laplacian on the Sierpinski lattices. First, we show that the spectrum of the Laplacian, as a subset of $\mathbb{C}$, remains the same for any $\ell^p$ spaces. Second, we characterize all the spectral points for the latti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f4c6360c4d15d0462bd42ef6106db562
https://doi.org/10.1007/s00041-021-09853-y
https://doi.org/10.1007/s00041-021-09853-y
Publikováno v:
Complex Analysis and Operator Theory
Complex Analysis and Operator Theory, Springer Verlag, 2020, ⟨10.1007/s11785-020-01053-8⟩
Complex Analysis and Operator Theory, Springer Verlag, 2020, ⟨10.1007/s11785-020-01053-8⟩
International audience; We study perturbations of the discrete Laplacian associated to discrete analogs of cusps and funnels. We perturb the metric and the potential in a long-range way. We establish a propagation estimate and a Limiting Absorption P
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::94a4e7f5b1732bc6ef25ba3ffb6c6b5a
https://hal.archives-ouvertes.fr/hal-02000996
https://hal.archives-ouvertes.fr/hal-02000996
Autor:
Korotyaev, Evgeny, Saburova, Natalia
Publikováno v:
Communications on Pure and Applied Analysis. 21:1691
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 total bandwidth for the Schrödinger operators in terms of geometric pa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1f0dba26a1f4c30e741a08c9f5da241f
https://doi.org/10.3934/cpaa.2022042
https://doi.org/10.3934/cpaa.2022042