We discuss the essential self-adjointness of wave operators, as well as the limiting absorption principle, in generalizations of asymptotically Minkowski settings. This is obtained via using a Fredholm framework for inverting the spectral family first, and then refining its conclusions to show dense range of $\Box-\lambda$, $\lambda\notin\mathbb R$, in $L^2_\mathrm {sc}$ when acting on an appropriate

We consider the problem of identifying a unitary Yang–Mills connection $\nabla$ on a Hermitian vector bundle from the Dirichlet-to-Neumann (DN) map of the connection Laplacian $\nabla^*\nabla$ over compact Riemannian manifolds with boundary. We establish uniqueness of the connection up to a gauge equivalence in the case of trivial line bundles in the smooth category and for the higher rank case in

It is shown that in a large class of disordered systems with singular alloy-type disorder and non-local media-particle interactions, the marginal measures of the induced random potential and the finite-volume integrated density of states (IDS) are infinitely differentiable in higher dimensions. The proposed approach complements the classical Wegner estimate which says that the IDS in the short-range

We consider resonances associated with excited eigenvalues of the cavity of a general Helmholtz resonator with straight neck. Under the assumption that the neck stays away from the nodal set of the corresponding eigenstate, we generalise the optimal exponential lower bound on the width of the resonance, that we have obtained in a previous paper for the ground resonance only.

In this paper we consider Anderson models with a large number of sites with zero interaction. For such models we study the spectral statistics in the region of complete localization. We show that Poisson statistics holds for such energies, by proving the Minami estimate.

This paper establishes by employing analytic and probabilistic techniques estimates concerning the heat content for the fractional Schrödinger operator $(-\Delta)^\frac {\alpha}{2} + c1_{\Omega}, c > 0$ with $0 < \alpha \leq 2$ in $\mathbb R^d$, $d \geq 2$ and $\Omega$ a Lebesgue measure set satisfying some regularity conditions.

We give examples of semiclassical Schrödinger operators with exponentially large cutoff resolvent norms, even when the supports of the cutoff and potential are very far apart. The examples are radial, which allows us to analyze the resolvent kernel in detail using ordinary differential equation techniques. In particular,we identify a threshold spatial radius where the resolvent behavior changes. We

We give an elementary proof of a weighted resolvent estimate for semiclassical Schrödinger operators in dimension $n \ge 1$. We require the potential belong to $L^\infty(\mathbb{R}^n)$ and have compact support, but do not require that it have distributional derivatives in $L^\infty(\mathbb{R}^n)$. The weighted resolvent norm is bounded by $e^{Ch^{-4/3}\log(h^{-1})}$, where $h$ is the semiclassical

We work with very general Banach spaces of analytic functions in the disk or other domains which satisfy a minimum number of natural axioms. Among the preliminary results, we discuss some implications of the basic axioms and identify all functional Banach spaces in which every bounded analytic function is a pointwise multiplier. Next, we characterize (in various ways) the weighted composition operators

In this paper, we investigate the anisotropic Calderón problem on cylindrical Riemannian manifolds with boundary having two ends and equipped with singular metrics ofwarped product type, that iswhose coefficients only depend on the horizontal direction of the cylinder. By singular, we mean that these coefficients are positive almost everywhere and belong to some $L^p, 1 \leq p \leq \infty$ spaces only

Let $H$ be a Schrödinger operator defined on a noncompact Riemannian manifold $\Omega$, and let $W\in L^\infty(\Omega;\mathbb{R})$. Suppose that the operator $H+W$ is critical in $\Omega$, and let $\varphi$ be the corresponding Agmon ground state. We prove that if $u$ is a generalized eigenfunction of $H$ satisfying $|u|\leq \varphi$ in $\Omega$, then the corresponding eigenvalue is in the spectrum

In this paper we discuss the relationship between the numerical range of an extensive class of unbounded operator functions and the joint numerical range of the operator coefficients. Furthermore, we derive methods on how to find estimates of the joint numerical range. Those estimates are used to obtain explicitly computable enclosures of the numerical range of the operator function and resolvent estimates

We provide examples of operators $T(D)+V$ in $L^2(\mathbb R^d)$ with decaying potentials that have embedded eigenvalues. The decay of the potential depends on the curvature of the (Fermi) surfaces of constant kinetic energy $T$. We make the connection to counterexamples in Fourier restriction theory.