Related papers: Propagation estimates in the one-commutator theory
Mourre's commutator theory is a powerful tool to study the continuous spectrum of self-adjoint operators and to develop scattering theory. We propose a new approach of its main result, namely the derivation of the limiting absorption…
We consider discrete Schr{\"o}dinger operators on ${\mathbb{Z}}^d$ for which the perturbation consists of the sum of a long-range type potential and a Wigner-von Neumann type potential. Still working in a framework of weighted Mourre…
The Propagation-Separation approach is an iterative procedure for pointwise estimation of local constant and local polynomial functions. The estimator is defined as a weighted mean of the observations with data-driven weights. Within…
Adapting Mourre's commutator method to the dissipative setting, we prove a limiting absorption principle for a class of abstract dissipative operators. A consequence is the resolvent estimates for the high frequency Helmholtz equation when…
We prove the limiting absorption principle on the non-compact interval $I$, on which the uniformly positive Mourre estimate holds. We reveal that such a result yields so-called smoothing estimates.
There are classical theorems of analysis which, given certain conditions on a perturbation, assert stability of the essential and absolutely continuous components of the spectrum of a self-adjoint operator. Whereas the singular component is…
We prove uniform resolvent estimates for an abstract operator given by a dissipative perturbation of a self-adjoint operator in the sense of forms. For this we adapt the commutators method of Mourre. We also obtain the limiting absorption…
Making use of the weighted Mourre theory developed in [GJ1], we show the limiting absorption principle for Schr{\"o}dinger operators with perturbed oscillating potential on appropriate energy intervals. We focus on a certain class of…
We apply weighted Mourre commutator theory to prove the limiting absorption principle for the discrete Schr{\"o}dinger operator perturbed by the sum of a Wigner-von Neumann and long-range type potential. In particular, this implies a new…
We study regularity of bound states pertaining to embedded eigenvalues of a self-adjoint operator $H$, with respect to an auxiliary operator $A$ that is conjugate to $H$ in the sense of Mourre. We work within the framework of singular…
The paper addresses state estimation for discrete-time systems with binary (threshold) measurements by following a Maximum A posteriori Probability (MAP) approach and exploiting a Moving Horizon (MH) approximation of the MAP cost-function.…
The present paper gives an abstract method to prove that possibly embedded eigenstates of a self-adjoint operator $H$ lie in the domain of the $k^{th}$ power of a conjugate operator $A$. Conjugate means here that $H$ and $A$ have a positive…
Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…
Radio map estimation (RME) is the problem of inferring the value of a certain metric (e.g. signal power) across an area of interest given a collection of measurements. While most works tackle this problem from a purely non-Bayesian…
According to standard econometric theory, Maximum Likelihood estimation (MLE) is the efficient estimation choice, however, it is not always a feasible one. In network diffusion models with unobserved signal propagation, MLE requires…
We study multistate Schr\"odinger operators related to molecular dynamics. We consider potentials which do not necessarily decay and prove absence of the singular continuous spectrum and propagation estimates which mean the scattering at…
We present a variant of Mourre's commutator theory. We apply it to prove the limiting absorption principle for Schr\"odinger operators with a perturbed Wigner-Von Neumann potential at suitable energies. To our knowledge, this result is new…
Propagation of error is a widely used estimation tool in experiments, where the estimation precision of the parameter depends on the fluctuation of the physical observable. Thus which observable is chosen will greatly affect the estimation…
We propose a rumor propagation model in which individuals within a homogeneously mixed population can assume one of infinitely many possible states. To analyze this model, we extend the classical law of large numbers for density-dependent…
On this short note, we apply the Mourre theory of the limiting absorption with {\it difference} type conditions on the potential, instead of conditions on the derivatives. In order that we modify the definition of the conjugate operator,…