## Search

Now showing items 1-10 of 12

#### Discrepancy of Minimal Riesz Energy Points

(2021-12-01)

We find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz s-energy on the sphere Sd. Our results are based on bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished ...

#### Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics

(2021-07-30)

In this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevrey-type spaces as time tends to infinity. Thus, echo chains are shown to ...

#### Static and Dynamical, Fractional Uncertainty Principles

(2021-03)

We study the process of dispersion of low-regularity solutions to the Schrödinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get ...

#### A pseudospectral method for the one-dimensional fractional Laplacian on R

(2021-01-15)

In this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over R, we map ...

#### Pointwise Convergence of the Schr\"odinger Flow

(2021-01)

In this paper we address the question of the pointwise almost everywhere limit of nonlinear Schr\"odinger flows to the initial data, in both the continuous and the periodic settings. Then we show how, in some cases, certain ...

#### Self-adjointness of two-dimensional Dirac operators on corner domains

(2021-01-01)

We investigate the self-adjointness of the two-dimensional Dirac operator D, with quantum-dot and Lorentz-scalar i-shell boundary conditions, on piecewise C2 domains (with finitely many corners). For both models, we prove ...

#### Dirac Operators and Shell Interactions: A Survey

(2021-01-01)

In this survey we gather recent results on Dirac operators coupled with δ-shell interactions. We start by discussing recent advances regarding the question of self-adjointness for these operators. Afterwards we switch to ...

#### On the Hausdorff dimension of Riemann's non-differentiable function

(2021-01-01)

Recent findings show that the classical Riemann's non-differentiable function has a physical and geometric nature as the irregular trajectory of a polygonal vortex filament driven by the binormal flow. In this article, we ...

#### Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow

(2021)

We consider the binormal flow equation, which is a model for the dynamics
of vortex filaments in Euler equations. Geometrically it is a flow of curves in three dimensions, explicitly connected to the 1-D Schr¨odinger map ...

#### On the one dimensional cubic NLS in a critical space

(2021)

In this note we study the initial value problem in a critical space for the one dimensional Schr¨odinger equation with a
cubic non-linearity and under some smallness conditions. In particular the initial data is given by ...