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  • A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator 

    Cassano B.; Pizzichillo F.; Vega L. (Revista Matemática Complutense, 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 ...
  • Evolution of Polygonal Lines by the Binormal Flow 

    Banica V.; Vega L. (Springer Nature Switzerland AG 2020, 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. ...
  • Some lower bounds for solutions of Schrodinger evolutions 

    Agirre M.; Vega L. (SIAM J. MATH. ANAL., 2019-08-21)
    We present some lower bounds for regular solutions of Schr odinger equations with bounded and time dependent complex potentials. Assuming that the solution has some positive mass at time zero within a ball of certain radius, ...
  • Uniqueness Properties of Solutions to the Benjamin-Ono equation and related models 

    Kenig E. C.; Ponce G.; Vega L. (2019-01-31)
    We prove that if u1, u2 are solutions of the Benjamin- Ono equation defined in (x, t) ∈ R × [0, T ] which agree in an open set Ω ⊂ R × [0,T], then u1 ≡ u2. We extend this uniqueness result to a general class of equations ...
  • 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 ...