Related papers: Spectral identities and smoothing estimates for ev…

We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies to nets of unitary operators, unitary representations of topological…

The purpose of the present work is to establish decorrelation estimates at distinct energies for some random Schr\"odinger operator in dimension one. In particular, we establish the result for some random operators on the continuum with…

The approximation of smooth functions with a spectral basis typically leads to rapidly decaying coefficients where the rate of decay depends on the smoothness of the function and vice-versa. The optimal number of degrees of freedom in the…

We consider evolution equations generated by quadratic operators admitting a decomposition in creation-annihilation operators without usual ellipticity-type hypotheses; this class includes hypocoercive model operators. We identify the…

In this paper we consider magnetic Schr\"odinger operators in R^n, n \ge 3. Under almost optimal conditions on the potentials in terms of decay and regularity we prove smoothing and Strichartz estimates, as well as a limiting absorption…

New estimates for eigenvalues of non-self-adjoint multi-dimensional Schr\"{o}dinger operators are obtained in terms of $L_{p}$-norms of the potentials. The results extend and improve those obtained previously. In particular, diverse…

We prove a family of identities that involve the solutions to the free Schreodinger equation. As a consequence of these identities we shall deduce a lower bound for the local smoothing estimate and a uniqueness criterion.

We will show that a local space-time estimate implies a global space-time estimate for dispersive operators. In order for this implication we consider a Littlewood-Paley type square function estimate for dispersive operators in a time…

We prove several new results on the absolutely continuous spectra of perturbed one-dimensional Stark operators. First, we find new classes of perturbations, characterized mainly by smoothness conditions, which preserve purely absolutely…

Given a self-adjoint involution J on a Hilbert space H, we consider a J-self-adjoint operator L=A+V on H where A is a possibly unbounded self-adjoint operator commuting with J and V a bounded J-self-adjoint operator anti-commuting with J.…

In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we develop an explicit scheme for constructing characteristic…

We develop a spectral cut-off construction of real-time oscillatory integrals associated with non-autonomous Hamiltonian evolution equations. Let \(H_0\) be a positive self-adjoint reference operator on a Hilbert space \(\Hilb\), and let…

We consider the Cauchy problem for a second-order evolution equation, in which the problem operator is the sum of two self-adjoint operators. The main feature of the problem is that one of the operators is represented in the form of the…

We introduce a new method to prove lower estimates for the approximation error of general linear operators with smooth range in terms of classical moduli of smoothness and related $K$-functionals. In addition, we explicitly show how to…

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…

The convergence of various operator splitting procedures, such as the sequential, the Strang and the weighted splitting, is investigated in the presence of a spatial approximation. To this end a variant of Chernoff's product formula is…

The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe some recent work of the authors which established sharp local…

We investigate $L^1(\mathbb R^n)\to L^\infty(\mathbb R^n)$ dispersive estimates for the Schr\"odinger operator $H=-\Delta+V$ when there is an eigenvalue at zero energy in even dimensions $n\geq 6$. In particular, we show that if there is an…

We give a refined description of the dominant spectrum of a non-local operator that models growth and equal mitosis of cells. More precisely we look at the spectrum in half planes at the right hand side of the first accumulation point of…

We establish global-in-time frequency localized local smoothing estimates for Schr\"odinger equations on hyperbolic space $\mathbb{H}^d$. In the presence of symmetric first and zeroth order potentials, which are possibly time-dependent,…