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Displaying 121 – 140 of 161

On the real analyticity of the scattering operator for the Hartree equation

Changxing Miao, Haigen Wu, Junyong Zhang (2009)

Annales Polonici Mathematici

We study the real analyticity of the scattering operator for the Hartree equation $i \partial_{t} u = - Δ u + u (V * | u | ²)$ . To this end, we exploit interior and exterior cut-off in time and space, together with a compactness argument to overcome difficulties which arise from absence of good properties as for the Klein-Gordon equation, such as the finite speed of propagation and ideal time decay estimate. Additionally, the method in this paper allows us to simplify the proof of analyticity of the scattering operator for the nonlinear...

On the Relative Completeness of the Generalized Eigenvectors of Elliptic Eigenvalue Problems with Indefinite Weight Functions.

Peter Hess (1985)

Mathematische Annalen

On the remainder in the Weyl formula for the Euclidean disk

Yves Colin de Verdière (2010/2011)

Séminaire de théorie spectrale et géométrie

We prove a 2-terms Weyl formula for the counting function $N (μ)$ of the spectrum of the Laplace operator in the Euclidean disk with a sharp remainder estimate $O (μ^{2 / 3})$ .

Currently displaying 121 – 140 of 161

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Displaying 121 – 140 of 161

On the real analyticity of the scattering operator for the Hartree equation

On the Relative Completeness of the Generalized Eigenvectors of Elliptic Eigenvalue Problems with Indefinite Weight Functions.

On the remainder in the Weyl formula for the Euclidean disk

On the scattering in Gevrey classes for the subcritical Hartree and Schrödinger equations

On the Scattering Matrix for N-Particle Hamiltonians

On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering.

On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators.

On the second eigenvalue of a Hardy-Sobolev operator.

On the singular set, the resolvent and Fermi's Golden Rule for finite volume hyperbolic surfaces.

On the S-matrix for Schrödinger operators with long-range potentials.

On the solvability of semilinear elliptic equation via an associated eigenvaule problem.

On the spectcral theory of elliptic differential operators. I.

On the Spectra of Schrödinger Operators with a Complex Potential.

On the spectral geometry of algebraic curves.

On the spectral theory of pseudo-differential elliptic boundary problems

On the spectrum and eigenfunctions of the Schrödinger operator with Aharonov–Bohm magnetic field.

On the spectrum of a nonlinear planar problem

On the Spectrum of Non-Compact Manifolds with Finite Volume.

On the spectrum of the negative Laplacian for general doubly-connected bounded domains.

On the spectrum of the $p$ -biharmonic operator.

Currently displaying 121 – 140 of 161