Browsing by Author "Vega, L."
Now showing items 1-20 of 42
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Absence of eigenvalues of two-dimensional magnetic Schr ̈odinger operators
Fanelli, L.; Krejcirik, D.; Vega, L.
(2017-10-17)
By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schr ̈odinger operator possesses no point ... -
Absence of eigenvalues of two-dimensional magnetic Schroedinger operators
Fanelli, L.; Krejcirik, D.; Vega, L. (2018-01-01)
By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schroedinger operator possesses no point ... -
An Isoperimetric-Type Inequality for Electrostatic Shell Interactions for Dirac Operators
Arrizabalaga, N.; Mas, A.; Vega, L. (2016-06-01)
In this article we investigate spectral properties of the coupling $H + V_{\lambda}$, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$, $m>0$ and $V_{\lambda}$ is an electrostatic shell ... -
Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
Correia, S.; Côte, R.; Vega, L. (2018-07-06)
We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. ... -
Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
Correia, S.; Côte, R.; Vega, L. (2018-07-06)
We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted W1,8 around a carefully chosen, two term ansatz. Such knowledge ... -
Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
Correia, S.; Côte, R.; Vega, L. (2020-05-01)
We give the asymptotics of the Fourier transform of self-similar solutions for the modified Korteweg-de Vries equation. In the defocussing case, the self-similar profiles are solutions to the Painlevé II equation; although ... -
Bilinear identities involving the $k$-plane transform and Fourier extension operators
Beltran, D.; Vega, L. (2019)
We prove certain $L^2(\mathbb{R}^n)$ bilinear estimates for Fourier extension operators associated to spheres and hyperboloids under the action of the $k$-plane transform. As the estimates are $L^2$-based, they follow from ... -
Bilinear identities involving the k-plane transform and Fourier extension operators
Beltran, D.; Vega, L. (2019-11-30)
We prove certain L2pRnq bilinear estimates for Fourier extension operators associ- ated to spheres and hyperboloids under the action of the k-plane transform. As the estimates are L2-based, they follow from bilinear ... -
Carleman type inequalities for fractional relativistic operators
Stan, D.; Roncal, L.; Vega, L. (2019-09-22)
In this paper, we derive Carleman estimates for the fractional relativistic operator. Firstly, we consider changing-sign solutions to the heat equation for such operators. We prove monotonicity inequalities and convexity ... -
Erratum to: Relativistic Hardy Inequalities in Magnetic Fields [J Stat Phys, 154, (2014), 866-876, DOI 10.1007/s10955-014-0915-0]
Fanelli, L.; Vega, L.; Visciglia, N. (2015-12-31)
[No abstract available] -
Evolution of Polygonal Lines by the Binormal Flow
Banica, V.; Vega, L. (2020-02-05)
The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr ̈odinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. ... -
Evolution of Polygonal Lines by the Binormal Flow
Banica, V.; Vega, L. (2020-06-01)
The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schrödinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. Finally ... -
Hardy uncertainty principle, convexity and parabolic evolutions
Escauriaza, L.; Kenig, C.E.; Ponce, G.; Vega, L. (2016-09-01)
We give a new proof of the $L^2$ version of Hardy’s uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of ... -
A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
Cassano, B.; Pizzichillo, F.; Vega, L. (2019-07-02)
We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials V of Coulomb type: we characterise ... -
A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator
Cassano, B.; Pizzichillo, F.; Vega, L. (2019-06)
We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials $\mathbf V$ of Coulomb type: ... -
A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator
Cassano, B.; Pizzichillo, F.; Vega, L. (2020-01-01)
We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials V of Coulomb type: we characterise ... -
On the energy of critical solutions of the binormal flow
Banica, V.; Vega, L. (2019-07-20)
The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisen- berg model in ferromagnetism, and the 1-D cubic Schr ... -
On the energy of critical solutions of the binormal flow
Banica, V.; Vega, L. (2020-07-02)
The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisenberg model in ferromagnetism, and the 1-D cubic ... -
On the Evolution of the Vortex Filament Equation for regular M-polygons with nonzero torsion
De la Hoz, F.; Kumar, S.; Vega, L. (2019-09-03)
In this paper, we consider the evolution of the Vortex Filament equa- tion (VFE): Xt = Xs ∧ Xss, taking M-sided regular polygons with nonzero torsion as initial data. Us- ing algebraic techniques, backed by numerical ... -
On the improvement of the Hardy inequality due to singular magnetic fields
Fanelli, L.; Krejcirik, D.; Laptev, A.; Vega, L. (2018-07-12)
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ...