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The class of Sturm-Liouville systems is defined. It appears to be a subclass of Riesz-spectral systems, since it is shown that the negative of a Sturm-Liouville operator is a Riesz-spectral operator on L^2(a,b) and the infinitesimal generator of a C_0-semigroup of bounded linear operators.

Sur le spectre de quelques opérateurs et les variétés de Jacobi

Henry P. McKean, Pierre van Moerbeke (1975/1976)

Séminaire Bourbaki

Sur l'inégalité de Sobolev logarithmique des opérateurs de Laguerre à petit paramètre

Laurent Miclo (2002)

Séminaire de probabilités de Strasbourg

The inverse spectral problem for the Sturm-Liouville operators with discontinuous coefficients.

Shestakov, A. I. (2003)

Sibirskij Matematicheskij Zhurnal

The monodromization and Harper equation

V. Buslaev, A. Fedotov (1993/1994)

Séminaire Équations aux dérivées partielles (Polytechnique)

The Montgomery model revisited

B. Helffer (2010)

Colloquium Mathematicae

We discuss the spectral properties of the operator $_{ℳ} (α) : = - d ² / d t ² + (1 / 2 t ² - α) ²$ on the line. We first briefly describe how this operator appears in various problems in the analysis of operators on nilpotent Lie groups, in the spectral properties of a Schrödinger operator with magnetic field and in superconductivity. We then give a new proof that the minimum over α of the groundstate energy is attained at a unique point and also prove that the minimum is non-degenerate. Our study can also be seen as a refinement for a specific...

The noncommutative Dirac equation for some wave functions.

Pişcoran, Laurian (2007)

Acta Universitatis Apulensis. Mathematics - Informatics

The width of resonances for slowly varying perturbations of one-dimensional periodic Schrödinger operators

Frédéric Klopp, Magali Marx (2005/2006)

Séminaire Équations aux dérivées partielles

Towards finite-gap integration of the Inozemtsev model.

Takemura, Kouichi (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Transitions d’Anderson pour des opérateurs de Schrödinger quasi-périodiques en dimension 1

Alexander Fedotov, Frédéric Klopp (1998/1999)

Séminaire Équations aux dérivées partielles

Two separation criteria for second order ordinary or partial differential operators

Richard C. Brown, Don B. Hinton (1999)

Mathematica Bohemica

We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in $ℝ^{n}$ . Also, for symmetric second-order ordinary differential operators we show that ${lim sup}_{t \to c} {(p q^{'})}^{'} / q^{2} = θ < 2$ where $c$ is a singular point guarantees separation of $- {(p y^{'})}^{'} + q y$ on its minimal domain and extend this criterion to the partial differential setting. As a particular example it is shown that $- Δ y + q y$ is separated on its minimal domain if $q$ is superharmonic. For $n = 1$ the criterion...

Zeros of eigenfunctions of some anharmonic oscillators

Alexandre Eremenko, Andrei Gabrielov, Boris Shapiro (2008)

Annales de l’institut Fourier

We study complex zeros of eigenfunctions of second order linear differential operators with real even polynomial potentials. For potentials of degree 4, we prove that all zeros of all eigenfunctions belong to the union of the real and imaginary axes. For potentials of degree 6, we classify eigenfunctions with finitely many zeros, and show that in this case too, all zeros are real or pure imaginary.

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Displaying 81 – 100 of 103

Spectral singularities of Sturm-Liouville problems with eigenvalue-dependent boundary conditions.

Spectral Theory for Slowly Oscillating Potentials I. Jacobi Matrices.

Stark resonances for random potentials of Anderson type

Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators

Sturm-Liouville operator with general boundary conditions.

Sturm-Liouville systems are Riesz-spectral systems