» Spectral analysis of The magnetic Laplacian acting on discrete funnels
09/07/25 09:00 from math.SP updates on arXiv.org
arXiv:2507.05766v1 Announce Type: cross Abstract: We study perturbations of the discrete magnetic Laplacian associated to discrete analogs of funnels. We perturb the metric in a long-range way. We establish a propagation estimate and a L...

» A Study of Kirk's Asymptotic Contractions via Leader Contractions
09/07/25 09:00 from math.FA updates on arXiv.org
arXiv:2507.05276v1 Announce Type: new Abstract: This paper investigates asymptotic fixed point results for nonlinear contractions, with emphasis on Kirk-type theorems and their generalizations. A central difficulty in the literature has ...

» Cauchy Data for 1D singular Schr\"odinger operators
09/07/25 09:00 from math.SP updates on arXiv.org
arXiv:2507.05772v1 Announce Type: cross Abstract: We study semiclassical 1D Schr\"odinger operators with a power-like singularity at $0$. We show that WKB expansions can be extended on any interval of the form [h^{1-},b]. Using a differe...

» On the Spectral Geometry and Small Time Mass of Anderson Models on Planar Domains
09/07/25 09:00 from math.SP updates on arXiv.org
arXiv:2507.06186v1 Announce Type: cross Abstract: We consider the Anderson Hamiltonian (AH) and the parabolic Anderson model (PAM) with white noise and Dirichlet boundary condition on a bounded planar domain $D\subset\mathbb R^2$. We com...

» A Low-Dimensional Counterexample to the HK-Conjecture
09/07/25 09:00 from math.OA updates on arXiv.org
arXiv:2507.05425v1 Announce Type: new Abstract: We provide a counterexample to the HK-conjecture using the flat manifold odometers constructed by Deeley. Deeley's counterexample uses an odometer built from a flat manifold of dimension 9 ...

» Certain Upper Bounds on the $A$-Numerical Radius of Operators in Semi-Hilbertian Spaces and Their Applications
09/07/25 09:00 from math.FA updates on arXiv.org
arXiv:2507.05398v1 Announce Type: new Abstract: Consider a complex Hilbert space $\left(\mathcal{H}, \langle \cdot, \cdot \rangle\right)$ equipped with a positive bounded linear operator $A$ on $\mathcal{H}$. This induces a semi-norm $\|...

» Spectral invariants for discrete Schr\"odinger operators on periodic graphs
09/07/25 09:00 from math.SP updates on arXiv.org
arXiv:2504.03282v2 Announce Type: replace Abstract: The aim of this article is to present a complete system of Floquet spectral invariants for the discrete Schr\"odinger operators with periodic potentials on periodic graphs. These invari...

» Perturbations of Toeplitz operators on vector-valued Hardy spaces
09/07/25 09:00 from math.FA updates on arXiv.org
arXiv:2507.05721v1 Announce Type: new Abstract: In this article, we completely classify invariant subspaces of certain finite-rank perturbations of Toeplitz operators on vector-valued Hardy spaces. As a byproduct, we describe invariant s...