Related papers: Spectral identities and smoothing estimates for ev…

This paper describes an approach to global smoothing problems for non-dispersive equations based on ideas of comparison principle and canonical transformation established in authors' previous paper, where dispersive equations were treated.…

We present a systematic treatment of scattering processes for quantum systems whose time evolution is discrete. We define and show some general properties of the scattering operator, in particular the conservation of quasi-energy which is…

This paper establishes a theory of nonlinear spectral decompositions by considering the eigenvalue problem related to an absolutely one-homogeneous functional in an infinite-dimensional Hilbert space. This approach is both motivated by…

In this paper we develop the classical multiplier technique to prove a virial identity and smoothing estimates (in a perturbative setting) for the electromagnetic variable coefficients Schroedinger equation.

We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…

We consider time-frequency localization operators $A_a^{\varphi_1,\varphi_2}$ with symbols $a$ in the wide weighted modulation space $ M^\infty_{w}(\mathbb{R}^{2d})$, and windows $ \varphi_1, \varphi_2 $ in the Gelfand-Shilov space…

This paper shows a simple construction of the continuous involutions of real intervals in terms of the continuous even functions. We also study the smooth involutions defined by symmetric equations. Finally, we review some applications, in…

This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lam\'e operators of elasticity $-\Delta^\ast + V$ in terms of suitable norms of the potential $V$. In…

Motivated by the long-time transport properties of quantum waves in weakly disordered media, the present work puts random Schr\"odinger operators into a new spectral perspective. Based on a stationary random version of a Floquet type…

A frequently occurring challenge in experimental and numerical observation is how to resolve features, such as spectral peaks - with center, width, height - and derivatives from measured data with unavoidable noise. Therefore, we develop a…

In the smooth scattering theory framework, we consider a pair of self-adjoint operators $H_0$, $H$ and discuss the spectral projections of these operators corresponding to the interval $(-\infty,\lambda)$. The purpose of the paper is to…

We discuss differential-- versus integral--equation based methods describing out--of thermal equilibrium systems and emphasize the importance of a well defined reduction to statistical observables. Applying the projection operator approach,…

In many practical applications of clustering, the objects to be clustered evolve over time, and a clustering result is desired at each time step. In such applications, evolutionary clustering typically outperforms traditional static…

In this paper we address smoothing-that is, optimisation-based-estimation techniques for localisation problems in the case where motion sensors are very accurate. Our mathematical analysis focuses on the difficult limit case where motion…

We consider evolution operators $G(t,s)$ associated to a class of nonautonomous elliptic operators with unbounded coefficients, in the space of bounded and continuous functions over $\mathbb{R}^d$. We prove some new pointwise estimates for…

This paper brings results about the behavior of sequences of eigenvalues or singular values of integral operators generated by square-integrable kernels on the real m-dimensional unit sphere, $m\leq2$. Under smoothness assumptions on the…

The vacuum expectation value of the evolution operator for a general class of Hamiltonians used in quantum field theory and statistical physics and which include unstable particles is considered. An exact formula which describes the large…

Strichartz estimates are a manifestation of a dispersion phenomenon, exhibited by certain partial differential equations, which is detected by suitable Lebesgue space norms. In most cases the evolution propagator $U(t)$ is a one parameter…

In this paper we study the convergence of a Lie-Trotter operator splitting for stochastic semi-linear evolution equations in a Hilbert space. The abstract Hilbert space setting allows for the consideration of convergence of the…

By making use of conformal mapping, we construct various time-evolution operators in (1+1) dimensional conformal field theories (CFTs), which take the form $\int dx\, f(x) \mathcal{H}(x)$, where $\mathcal{H}(x)$ is the Hamiltonian density…