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Displaying 241 – 260 of 591

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On non-overdetermined inverse scattering at zero energy in three dimensions

Roman G. Novikov (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We develop the ¯ -approach to inverse scattering at zero energy in dimensions d 3 of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction procedure, stability estimate and approximate reconstruction for the problem of finding a sufficiently small potential v in the Schrödinger equation from a fixed non-overdetermined (“backscattering” type) restriction h | Γ of the Faddeev generalized scattering amplitude h in the...

On solutions of the Schrödinger equation with radiation conditions at infinity : the long-range case

Yannick Gâtel, Dimitri Yafaev (1999)

Annales de l'institut Fourier

We consider the homogeneous Schrödinger equation with a long-range potential and show that its solutions satisfying some a priori bound at infinity can asymptotically be expressed as a sum of incoming and outgoing distorted spherical waves. Coefficients of these waves are related by the scattering matrix. This generalizes a similar result obtained earlier in the short-range case.

On some new spectral estimates for Schrödinger-like operators

Daniel Levin (2006)

Open Mathematics

We prove the analog of the Cwikel-Lieb-Rozenblum estimate for a wide class of second-order elliptic operators by two different tools: Lieb-Thirring inequalities for Schrödinger operators with matrix-valued potentials and Sobolev inequalities for warped product spaces.

On the Bethe-Sommerfeld conjecture

Leonid Parnovski, Alexander V. Sobolev (2000)

Journées équations aux dérivées partielles

We consider the operator in d , d 2 , of the form H = ( - Δ ) l + V , l > 0 with a function V periodic with respect to a lattice in d . We prove that the number of gaps in the spectrum of H is finite if 8 l > d + 3 . Previously the finiteness of the number of gaps was known for 4 l > d + 1 . Various approaches to this problem are discussed.

On the Dirichlet problem associated with the Dunkl Laplacian

Mohamed Ben Chrouda (2016)

Annales Polonici Mathematici

This paper deals with the questions of the existence and uniqueness of a solution to the Dirichlet problem associated with the Dunkl Laplacian Δ k as well as the hypoellipticity of Δ k on noninvariant open sets.

On the dynamic behavior and stability of controlled connected Rayleigh beams under pointwise output feedback

Bao-Zhu Guo, Jun-Min Wang, Cui-Lian Zhou (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We study the dynamic behavior and stability of two connected Rayleigh beams that are subject to, in addition to two sensors and two actuators applied at the joint point, one of the actuators also specially distributed along the beams. We show that with the distributed control employed, there is a set of generalized eigenfunctions of the closed-loop system, which forms a Riesz basis with parenthesis for the state space. Then both the spectrum-determined growth condition and exponential stability...

On the equivalence of Green functions for general Schrödinger operators on a half-space

Abdoul Ifra, Lotfi Riahi (2004)

Annales Polonici Mathematici

We consider the general Schrödinger operator L = d i v ( A ( x ) x ) - μ on a half-space in ℝⁿ, n ≥ 3. We prove that the L-Green function G exists and is comparable to the Laplace-Green function G Δ provided that μ is in some class of signed Radon measures. The result extends the one proved on the half-plane in [9] and covers the case of Schrödinger operators with potentials in the Kato class at infinity K considered by Zhao and Pinchover. As an application we study the cone L ( ) of all positive L-solutions continuously vanishing...

Currently displaying 241 – 260 of 591