Spectral properties of Schrödinger operators on perturbed lattices

K Ando, H Isozaki, H Morioka - Annales Henri Poincaré, 2016 - Springer
We study the spectral properties of Schrödinger operators on perturbed lattices. We shall
prove the non-existence or the discreteness of embedded eigenvalues, the limiting …

Scattering on periodic metric graphs

E Korotyaev, N Saburova - Reviews in Mathematical Physics, 2020 - World Scientific
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 …

Continuum limit for lattice Schrödinger operators

H Isozaki, A Jensen - Reviews in Mathematical Physics, 2022 - World Scientific
We study the behavior of solutions of the Helmholtz equation (− Δ disc, h− E) uh= fh on a
periodic lattice as the mesh size h tends to 0. Projecting to the eigenspace of a characteristic …

[图书][B] Inverse Spectral and Scattering Theory: An Introduction

H Isozaki - 2020 - Springer
1. Inverse Spectral Problems Waves propagate carrying characteristic features of
surrounding media, more generally, ambient spaces. By observing the wave motion, one …

Gelfand's inverse problem for the graph Laplacian

E Blåsten, H Isozaki, M Lassas, J Lu - Journal of Spectral Theory, 2023 - ems.press
Gelfand’s inverse problem for the graph Laplacian Page 1 J. Spectr. Theory 13 (2023), 1–45
DOI 10.4171/JST/455 © 2023 European Mathematical Society Published by EMS Press This …

Inverse spectral problem for the Schrödinger operator on the square lattice

D Wu, CF Yang, NP Bondarenko - Inverse Problems, 2024 - iopscience.iop.org
We consider an inverse spectral problem on a quantum graph associated with the square
lattice. Assuming that the potentials on the edges are compactly supported and symmetric …

A Calderón type inverse problem for tree graphs

H Gernandt, J Rohleder - Linear Algebra and its Applications, 2022 - Elsevier
We study the inverse problem of recovering a tree graph together with the weights on its
edges (equivalently a metric tree) from the knowledge of the Dirichlet-to-Neumann matrix …

Continuum limit for Laplace and Elliptic operators on lattices

K Mikami, S Nakamura, Y Tadano - Pure and Applied Analysis, 2024 - msp.org
Continuum limits of Laplace operators on general lattices are considered, and it is shown
that these operators converge to elliptic operators on the Euclidean space in the sense of …

Inverse problems for quantum graph associated with square and hexagonal lattices

K Ando, E Blåsten, P Exner, H Isozaki… - arXiv preprint arXiv …, 2024 - arxiv.org
arXiv:2409.02605v1 [math-ph] 4 Sep 2024 Page 1 arXiv:2409.02605v1 [math-ph] 4 Sep 2024
INVERSE PROBLEMS FOR QUANTUM GRAPH ASSOCIATED WITH SQUARE AND …

Spectral and scattering theory for topological crystals perturbed by infinitely many new edges

S Richard, N Tsuzu - Reviews in Mathematical Physics, 2022 - World Scientific
In this paper, we investigate the spectral and scattering theory for operators acting on
topological crystals and on their perturbations. Special attention is paid to perturbations …