Related papers: Low energy resolvent expansions in dimension two
We compute low energy asymptotics for the resolvent of the Aharonov--Bohm Hamiltonian with multiple poles for both integer and non-integer total fluxes. For integral total flux we reduce to prior results in black-box scattering while for…
We compute low energy asymptotics for the resolvent of a planar obstacle, and deduce asymptotics for the corresponding scattering matrix, scattering phase, and exterior Dirichlet-to-Neumann operator. We use an identity of Vodev to relate…
We prove low frequency resolvent estimates and local energy decay for the Schr{\"o}dinger equation in an asymptotically Euclidean setting. More precisely, we go beyond the optimal estimates by comparing the resolvent of the perturbed…
In this paper we describe a new method for analyzing the Laplacian on asymptotically hyperbolic spaces, which was introduced recently by the author. This new method in particular constructs the analytic continuation of the resolvent for…
We consider self-adjoint operators of black-box type which are exponentially close to the free Laplacian near infinity, and prove an exponential bound for the resolvent in a strip away from resonances. Here the resonances are defined as…
We describe wave decay rates associated to embedded resonances and spectral thresholds for waveguides and manifolds with infinite cylindrical ends. We show that if the cut-off resolvent is polynomially bounded at high energies, as is the…
We prove a limiting absorption principle at zero energy for two-body Schr\"odinger operators with long-range potentials having a positive virial at infinity. More precisely, we establish a complete asymptotic expansion of the resolvent in…
On an asymptotically conic manifold $(M,g)$, we analyze the asymptotics of the integral kernel of the resolvent $R_q(k):=(\Delta_q+k^2)^{-1}$ of the Hodge Laplacian $\Delta_q$ on $q$-forms as the spectral parameter $k$ approaches zero,…
We consider manifolds with conic singularites that are isometric to $\mathbb{R}^{n}$ outside a compact set. Under natural geometric assumptions on the cone points, we prove the existence of a logarithmic resonance-free region for the…
We quantify the subcriticality of the bilaplacian in dimensions greater than four by providing explicit repulsivity/smallness conditions on complex additive perturbations under which the spectrum remains stable. Our assumptions cover…
We prove a general abstract theorem deducing wave expansions as time goes to infinity from resolvent expansions as energy goes to zero, under an assumption of polynomial boundedness of the resolvent at high energy. We give applications to…
We study the low energy resolvent of the Hodge Laplacian on a manifold equipped with a fibred boundary metric. We determine the precise asymptotic behavior of the resolvent as a fibred boundary (aka $\phi$-) pseudodifferential operator when…
In this paper, we mainly discuss asymptotic profiles of solutions to a class of abstract second-order evolution equations of the form $u''+Au+u'=0$ in real Hilbert spaces, where $A$ is a nonnegative selfadjoint operator. The main result is…
We present an explicit formula for the resolvent of the discrete Laplacian on the square lattice, and compute its asymptotic expansions around thresholds in low dimensions. As a by-product we obtain a closed formula for the fundamental…
We establish logarithmic local energy decay for wave equations with a varying wavespeed in dimensions two and higher, where the wavespeed is assumed to be a short range perturbation of unity with mild radial regularity. The key ingredient…
We develop a resolvent-based self-consistent framework for strongly correlated many-body systems by reorganizing many-body expansions at the level of the resolvent rather than through perturbative expansions in a small parameter. Starting…
In this paper we develop certain aspects of perturbation theory for self-adjoint operators subject to small variations of their domains. We use the abstract theory of boundary triplets to quantify such perturbations and give the second…
We investigate the low-energy behavior of the resolvent of Schrodinger operators with finitely many point interactions in three dimensions. We also discuss the occurrence and the multiplicity of zero energy obstructions.
This is an expository paper about self-adjoint extensions of the Laplacian on R^d, initially defined on functions supported away from a point. Let L be the Laplacian with domain smooth functions with compact support away from the origin. We…
We use a Lagrangian regularity perspective to discuss resolvent estimates near zero energy on Riemannian scattering, i.e. asymptotically conic, spaces, and their generalizations. In addition to the Lagrangian perspective we introduce and…