Browsing by Author "Sambou, Diomba"

Now showing 1 - 6 of 6
  • No Thumbnail Available
    Item
    A criterion for the existence of nonreal eigenvalues for a Dirac operator
    (2016) Sambou, Diomba
    The aim of this work is to explore the discrete spectrum generated by complex perturbations in L-2 (R-3, C-4) of the 3d Dirac operator
  • No Thumbnail Available
    Item
    Counting Function of Magnetic Resonances for Exterior Problems
    (2016) Bruneau, Vincent; Sambou, Diomba
    We study the asymptotic distribution of the resonances near the Landau levels , , of the Dirichlet (resp. Neumann, resp. Robin) realization in the exterior of a compact domain of of the 3D Schrodinger operator with constant magnetic field of scalar intensity . We investigate the corresponding resonance counting function and obtain the main asymptotic term. In particular, we prove the accumulation of resonances at the Landau levels and the existence of resonance-free sectors. In some cases, it provides the discreteness of the set of embedded eigenvalues near the Landau levels.
  • No Thumbnail Available
    Item
    Logarithmic stability inequality in an inverse source problem for the heat equation on a waveguide
    (2020) Kian, Yavar; Sambou, Diomba; Soccorsi, Eric
    We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with homogeneous initial and Dirichlet data.
  • Thumbnail Image
    Item
    On eigenvalue accumulation for non-self-adjoint magnetic operators
    (ELSEVIER SCIENCE BV, 2017) Sambou, Diomba
    In this work, we use regularized determinants to study the discrete spectrum generated by relatively compact non-self-adjoint perturbations of the magnetic Schrodinger operator (-i del - A)(2) -b in R-3, with constant magnetic field of strength b > 0. The distribution of the above discrete spectrum near the Landau levels 2bq, q is an element of N, is more interesting since they play the role of thresholds of the spectrum of the free operator. First, we obtain sharp upper bounds on the number of complex eigenvalues near the Landau levels. Under appropriate hypothesis, we then prove the presence of an infinite number of complex eigenvalues near each Landau level 2bq, q is an element of N, and the existence of sectors free of complex eigenvalues. We also prove that the eigenvalues are localized in certain sectors adjoining the Landau levels. In particular, we provide an adequate answer to the open problem from [34] about the existence of complex eigenvalues accumulating near the Landau levels. Furthermore, we prove that the Landau levels are the only possible accumulation points of the complex eigenvalues. (C) 2016 Elsevier Masson SAS. All rights reserved.
  • No Thumbnail Available
    Item
    Spectral analysis near the low ground energy of magnetic Pauli operators
    (2016) Sambou, Diomba
    We are interested in 3-D magnetic Pauli operators perturbed by a 2 x 2 Hermitian matrix-valued potential V = V(x), x is an element of R-3. We extend to the Pauli case the Breit-Wigner-type approximation and trace formula results obtained for the 3-D Schrodinger operator near the Landau levels. Hence, we give a link between the resonances and the spectral shift function near the low ground energy of the operators. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
  • No Thumbnail Available
    Item
    Spectral non-self-adjoint analysis of complex Dirac, Pauli and Schrodinger operators with constant magnetic fields of full rank
    (2019) Sambou, Diomba
    We consider Dirac, Pauli and Schrodinger quantum Hamiltonians with constant magnetic fields of full rank in L-2(R-2d), d >= 1, perturbed by non-self-adjoint (matrix-valued) potentials. On the one hand, we show the existence of non-self-adjoint perturbations, generating near each point of the essential spectrum of the operators, infinitely many (complex) eigenvalues. On the other hand, we give asymptotic behaviours of the number of the (complex) eigenvalues. In particular, for compactly supported potentials, our results establish non-self-adjoint extensions of Raikov-Warzel [Rev. in Math. Physics 14 (2002), 1051-1072] and Melgaard-Rozenblum [Commun. PDE. 28 (2003), 697-736] results. So, we show how the (complex) eigenvalues converge to the points of the essential spectrum asymptotically, i.e., up to a multiplicative explicit constant, as