Displaying similar documents to “A minimax principle for eigenvalues in spectral gaps: Dirac operators with Coulomb potentials.”

Algebraic spectral gaps

Amaury Mouchet (2012)

ESAIM: Proceedings

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For the one-dimensional Schrödinger equation, some real intervals with no eigenvalues (the spectral gaps) may be obtained rather systematically with a method proposed by H. Giacomini and A. Mouchet in 2007. The present article provides some alternative formulation of this method, suggests some possible generalizations and extensively discusses the higher-dimensional case.

General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators

Jean Dolbeault, Maria Esteban, Eric Séré (2006)

Journal of the European Mathematical Society

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This paper is concerned with an extension and reinterpretation of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. We state two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then these results are applied to Dirac operators in order to characterize simultaneously eigenvalues corresponding to electronic and positronic bound states.

On the characterization of scalar type spectral operators

P. A. Cojuhari, A. M. Gomilko (2008)

Studia Mathematica

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The paper is concerned with conditions guaranteeing that a bounded operator in a reflexive Banach space is a scalar type spectral operator. The cases where the spectrum of the operator lies on the real axis and on the unit circle are studied separately.

Dynamical Resonances and SSF Singularities for a Magnetic Schrödinger Operator

Astaburuaga, María Angélica, Briet, Philippe, Bruneau, Vincent, Fernández, Claudio, Raikov, Georgi (2008)

Serdica Mathematical Journal

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We consider the Hamiltonian H of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator H has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb H by appropriate scalar potentials V and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable...

Discrete spectrum and principal functions of non-selfadjoint differential operator

Gülen Başcanbaz Tunca, Elgiz Bairamov (1999)

Czechoslovak Mathematical Journal

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In this article, we consider the operator L defined by the differential expression ℓ ( y ) = - y ' ' + q ( x ) y , - ∞ < x < ∞ in L 2 ( - ∞ , ∞ ) , where q is a complex valued function. Discussing the spectrum, we prove that L has a finite number of eigenvalues and spectral singularities, if the condition sup - ∞ < x < ∞ exp ϵ | x | | q ( x ) | < ∞ , ϵ > 0 holds. Later we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities.

On unbounded hyponormal operators III

J. Janas (1994)

Studia Mathematica

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The paper deals mostly with spectral properties of unbounded hyponormal operators. Some nontrivial examples of such operators are given.