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Displaying 21 – 40 of 43

The Role of Green’s Functions in Inverse Scattering at Fixed Energy

James Ralston (1996/1997)

Séminaire Équations aux dérivées partielles

The Schrödinger equation on a compact manifold : Strichartz estimates and applications

Nicolas Burq, Patrick Gérard, Nikolay Tzvetkov (2001)

Journées équations aux dérivées partielles

We prove Strichartz estimates with fractional loss of derivatives for the Schrödinger equation on any riemannian compact manifold. As a consequence we infer global existence results for the Cauchy problem of nonlinear Schrödinger equations on surfaces in the case of defocusing polynomial nonlinearities, and on three-manifolds in the case of quadratic nonlinearities. We also discuss the optimality of these Strichartz estimates on spheres.

The spaces of quantum states for some harmonic oscillator potentials on the punctured plane C∖{0}

Jan Milewski (2007)

Banach Center Publications

We consider equivariant solutions of Schrödinger equations on C∖{0} with harmonic oscillator potentials. We determine the spaces of equivariant quantum states in three cases: for an isotropic and anisotropic harmonic oscillator potential centered at 0, and for a potential not centered at 0.

The spectral cutting problem

M. Burnat (1982)

Banach Center Publications

The spectral properties of the Schrödinger operator in nonseparable Hilbert spaces

M. Burnat (1982)

Banach Center Publications

The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential.

M.M. Skriganov (1985)

Inventiones mathematicae

The spectrum of Schrödinger operators with random $δ$ magnetic fields

Takuya Mine, Yuji Nomura (2009)

Annales de l’institut Fourier

We shall consider the Schrödinger operators on $ℝ^{2}$ with the magnetic field given by a nonnegative constant field plus random $δ$ magnetic fields of the Anderson type or of the Poisson-Anderson type. We shall investigate the spectrum of these operators by the method of the admissible potentials by Kirsch-Martinelli. Moreover, we shall prove the lower Landau levels are infinitely degenerated eigenvalues when the constant field is sufficiently large, by estimating the growth order of the eigenfunctions...

The Spectrum of the Continuous Laplacian on a Graph.

Carla Cattaneo (1997)

Monatshefte für Mathematik

The trace inequality and eigenvalue estimates for Schrödinger operators

R. Kerman, Eric T. Sawyer (1986)

Annales de l'institut Fourier

Suppose $Φ$ is a nonnegative, locally integrable, radial function on $R^{n}$ , which is nonincreasing in $| x |$ . Set $(T f) (x) = \int_{R^{n}} Φ (x - y) f (y) d y$ when $f \geq 0$ and $x \in R^{n}$ . Given $1 < p < \infty$ and $v \geq 0$ , we show there exists $C > 0$ so that $\int_{R^{n}} (T f) (x)^{p} v (x) d x \leq C \int_{R^{n}} f (x)^{p} d x$ for all $f \geq 0$ , if and only if $C^{'} > 0$ exists with $\int_{Q} T (x_{Q} v) (x)^{p^{'}} d x \leq C^{'} \int_{Q} v (x) d x < \infty$ for all dyadic cubes Q, where $p^{'} = p / (p - 1)$ . This result is used to refine recent estimates of C.L. Fefferman and D.H. Phong on the distribution of eigenvalues of Schrödinger operators.