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  • 1.
    Frank, Rupert L.
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Safronov, Oleg
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Absolutely continuous spectrum of a class of random nonergodic Schrodinger operators2005In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, no 42, p. 2559-2577Article in journal (Refereed)
  • 2.
    Laptev, Ari
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Naboko, S.
    Safronov, Oleg
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials2005In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 253, no 3, p. 611-631Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to extend a class of potentials for which the absolutely continuous spectrum of the corresponding multidimensional Schrodinger operator is essentially supported by [0, infinity). Our main theorem states that this property is preserved for slowly decaying potentials provided that there are some oscillations with respect to one of the variables.

  • 3. Laptev, Ari
    et al.
    Safronov, Oleg
    Eigenvalue Estimates for Schrodinger Operators with Complex Potentials2009In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 292, no 1, p. 29-54Article in journal (Refereed)
    Abstract [en]

    We discuss properties of eigenvalues of non-self-adjoint Schrodinger operators with complex-valued potential V. Among our results are estimates of the sum of powers of imaginary parts of eigenvalues by the L-p-norm of JV.

  • 4.
    Laptev, Ari
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Safronov, Oleg
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    The negative discrete spectrum of a class of two-dimensional Schrödinger operators with magnetic fields2005In: Asymptotic Analysis, ISSN 0921-7134, E-ISSN 1875-8576, Vol. 41, no 2, p. 107-117Article in journal (Refereed)
    Abstract [en]

    We obtain an asymptotic formula for the number of negative eigenvalues of a class of two-dimensional Schrodinger operators with small magnetic fields. This number increases as a coupling constant of the magnetic field tends to zero.

  • 5.
    Safronov, Oleg
    KTH, Superseded Departments, Mathematics.
    The amount of discrete spectrum of a perturbed periodic Schrodinger operator inside a fixed interval (lambda(1),lambda(2))2004In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, no 9, p. 411-423Article in journal (Refereed)
    Abstract [en]

    Let A be a periodic Schrödinger operator and let V ≥ 0 be a decaying potential. We study the number of the eigenvalues of the operator A(α)=A−α V inside a fixed interval (λ12). We obtain an asymptotic formula for as α → ∞. In this paper we extend the results of Safronov (2001) for a more general class of perturbations.

  • 6.
    Safronov, Oleg
    KTH, Superseded Departments, Mathematics.
    The spectral measure of a Jacobi matrix in terms of the Fourier transform of the perturbation2004In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 42, no 2, p. 363-377Article in journal (Refereed)
    Abstract [en]

    We study the spectral properties of Jacobi matrices. By combining Killip's technique [12] with the technique of Killip and Simon [13] we obtain a result relating the properties of the elements of Jacobi matrices and the corresponding spectral measures. This theorem is a natural extension of a recent result of Laptev-Naboko-Safronov [17].

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