Unique continuation and lifting of spectral band edges of Schrödinger operators on unbounded domains
From MaRDI portal
Publication:2662227
DOI10.4171/JST/314zbMath1461.35171arXiv1804.07816OpenAlexW3080304082MaRDI QIDQ2662227
Ivica Nakić, Martin Tautenhahn, Ivan Veselić, Matthias Täufer
Publication date: 9 April 2021
Published in: Journal of Spectral Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1804.07816
uncertainty principleunique continuationspectral edgeslifting estimatessemi-definite perturbationspectral engineering
Estimates of eigenvalues in context of PDEs (35P15) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Continuation and prolongation of solutions to PDEs (35B60)
Related Items
Geometry, dynamics and spectrum of operators on discrete spaces. Abstracts from the workshop held January 3--9, 2021 (online meeting), An abstract Logvinenko-Sereda type theorem for spectral subspaces, Uncertainty principles with error term in Gelfand-Shilov spaces, Unique continuation for the gradient of eigenfunctions and Wegner estimates for random divergence-type operators, Quantitative unique continuation for spectral subspaces of Schrödinger operators with singular potentials, Scale-free unique continuation estimates and Logvinenko-Sereda theorems on the torus, Lower bounds for Dirichlet Laplacians and uncertainty principles, On a minimax principle in spectral gaps
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Sampling inequality for \(L^2\)-norms of eigenfunctions, spectral projectors, and Weyl sequences of Schrödinger operators
- Bounds on the density of states for Schrödinger operators
- Unique continuation principle for spectral projections of Schrödinger operators and optimal Wegner estimates for non-ergodic random Schrödinger operators
- Notes on the \(\sin 2\Theta\) theorem
- Scale-free uncertainty principles and Wegner estimates for random breather potentials
- Null-controllability of the Kolmogorov equation in the whole phase space
- Some results on controllability for linear and nonlinear heat equations in unbounded domains
- Perturbation of spectral subspaces and solution of linear operator equations
- A minimax principle for eigenvalues in spectral gaps: Dirac operators with Coulomb potentials.
- Discrete spectrum of the perturbed Dirac operator
- Sharp geometric condition for null-controllability of the heat equation on \(\mathbb R^d\) and consistent estimates on the control cost
- On an estimate in the subspace perturbation problem
- Scale-free unique continuation principle for spectral projectors, eigenvalue-lifting and Wegner estimates for random Schrödinger operators
- Unique continuation estimates for the Laplacian and the heat equation on non-compact manifolds
- A comprehensive proof of localization for continuous Anderson models with singular random potentials
- Scale-free and quantitative unique continuation for infinite dimensional spectral subspaces of Schrödinger operators
- Scale-free unique continuation estimates and applications to random Schrödinger operators
- On the null-controllability of the heat equation in unbounded domains
- Observable set, observability, interpolation inequality and spectral inequality for the heat equation in \(\mathbb{R}^n\)
- Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices
- On the minimax principle for Coulomb-Dirac operators
- Notes on the subspace perturbation problem for off-diagonal perturbations
- Discrete Spectrum of the Periodic Schrödinger Operator with a Variable Metric Perturbed by a Nonnegative Potential
- Spectral perturbation bounds for selfadjoint operators I
- Localization for random perturbations of periodic Schrödinger operators
- Null-controllability of hypoelliptic quadratic differential equations
- Sharp estimates and homogenization of the control cost of the heat equation on large domains
- Exact null internal controllability for the heat equation on unbounded convex domains
- The Rotation of Eigenvectors by a Perturbation. III
- Triple variational principles for self-adjoint operator functions
