相关论文: A note on the Schr\"odinger smoothing effect

A calculation of the Sommerfeld enhancement is presented and applied to the problem of s-wave non-relativistic dark matter annihilation. The difference from previous computations in the literature is that the effect of the underlying…

In this paper, by constructing the weight functions, a global Carleman estimate for the Schrodinger equation on a tree is established, with a strong assumption on the solution. And the estimate is able to be applied to derive the Lipschitz…

We consider the problem of estimating the mean vector $\theta$ of a $d$-dimensional spherically symmetric distributed $X$ based on balanced loss functions of the forms: {\bf (i)} $\omega \rho(\|\de-\de_{0}\|^{2}) +(1-\omega)\rho(\|\de -…

We consider the effects of a light quark mass in the soft-collinear effective theory (SCET) and we apply them to B -> X_s gamma in the endpoint region. We find that the reparameterization invariance can be extended by including the…

In this paper, we improve slightly Erd\'elyi's version of the stationary phase method by replacing the employed smooth cut-off function by a characteristic function, leading to more precise remainder estimates. We exploit this refinement to…

The purpose of this note is to prove global-in-time smoothing effects for the Schr\"odinger equation with potentials exhibiting critical singularity. A typical example of admissible potentials is the inverse-square potential $a|x|^{-2}$…

The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…

We investigate whether a fundamental solution of the Schr\"odinger equation $\partial_t u =(\Delta +V)\, u$ has local in time sharp Gaussian estimates. We compare that class with the class of $V$ for which local in time plain Gaussian…

Quantum-gravity corrections (in the form of a minimal length) to the Feynman propagator for a free scalar particle in $\mathbb{R}^D$ are shown to be the result of summing over all dimensions $D'\geq D$ of $\mathbb{R}^{D'}$, each summand…

A generalization of the Yang-Baxter equation is proposed. It enables to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit…

In this paper we obtain a pointwise sparse domination for generalized H\"ormander operators and also for iterated commutators with those operators. As a particular case of our result we obtain a extension of the sparse domination for…

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…

We prove weighted $L^2$ estimates for the Klein-Gordon equation perturbed with singular potentials such as the inverse-square potential. We then deduce the well-posedness of the Cauchy problem for this equation with small perturbations, and…

We consider the defocusing nonlinear Schr{\"o}dinger equation with a gauge invariant power-like nonlinearity. We prove global dispersive estimates in a semi-classical scaling, after rescaling the solution thanks to a suitable distorsion of…

The propagator of the discrete Schr\"odinger equation is computed and its properties are revealed through a Feynman path summation in discrete space. Initial data problems such as diffraction in discrete space and continuous time are…

We introduce a kernel estimator, to the tail index of a right-censored Pareto-type distribution, that generalizes Worms's one (Worms and Worms, 2014)in terms of weight coefficients. Under some regularity conditions, the asymptotic normality…

In this paper we prove that in appropriate weighted Sobolev spaces, in the case of no bound states, the scattering map of the Korteweg-de Vries (KdV) on $\mathbb R$ is a perturbation of the Fourier transform by a regularizing operator. As…

A generalized Tomonaga--Schwinger equation, holding on the entire boundary of a {\em finite} spacetime region, has recently been considered as a tool for studying particle scattering amplitudes in background-independent quantum field…

We consider second order differential operators with coefficients which are Gaussian random fields. When the covariance becomes singular at short distances then the propagators of the Schr\"odinger equation as well as of the wave equation…

This paper is devoted to the study of quantitative weighted norm estimates for martingale square functions in both scalar-weighted and matrix-weighted settings. In particular, we introduce the martingale square functions $S_W$ via matrix…