Radiation conditions and scattering theory for -particle hamiltonians (main ideas of the approach)
Radiation conditions and scattering theory for -particle quantum systems
Radiation conditions at the top of a rotational cusp in the theory of water-waves
We study the linearized water-wave problem in a bounded domain (e.g.a finite pond of water) of , having a cuspidal boundary irregularity created by a submerged body. In earlier publications the authors discovered that in this situation the spectrum of the problem may contain a continuous component in spite of the boundedness of the domain. Here, we proceed to impose and study radiation conditions at a point of the water surface, where a submerged body touches the surface (see Fig. 1). The radiation...
Radiation conditions at the top of a rotational cusp in the theory of water-waves
We study the linearized water-wave problem in a bounded domain (e.g. a finite pond of water) of , having a cuspidal boundary irregularity created by a submerged body. In earlier publications the authors discovered that in this situation the spectrum of the problem may contain a continuous component in spite of the boundedness of the domain. Here, we proceed to impose and study radiation conditions at a point of the water surface, where a submerged body touches the surface (see Fig. 1)....
RAGE theorem for power bounded operators and decay of local energy for moving obstacles
Rational invariant tori, phase space tunneling, and spectra for non-selfadjoint operators in dimension
We study spectral asymptotics and resolvent bounds for non-selfadjoint perturbations of selfadjoint -pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part is completely integrable. Spectral contributions coming from rational invariant Lagrangian tori are analyzed. Estimating the tunnel effect between strongly irrational (Diophantine) and rational tori, we obtain an accurate description of the spectrum in a suitable complex window, provided that the...
Rational Krylov for nonlinear eigenproblems, an iterative projection method
In recent papers Ruhe suggested a rational Krylov method for nonlinear eigenproblems knitting together a secant method for linearizing the nonlinear problem and the Krylov method for the linearized problem. In this note we point out that the method can be understood as an iterative projection method. Similarly to the Arnoldi method the search space is expanded by the direction from residual inverse iteration. Numerical methods demonstrate that the rational Krylov method can be accelerated considerably...
Reaction-diffusion problems in cylinders with no invariance by translation. Part II : monotone perturbations
Recent results on Lieb-Thirring inequalities
We give a survey of results on the Lieb-Thirring inequalities for the eigenvalue moments of Schrödinger operators. In particular, we discuss the optimal values of the constants therein for higher dimensions. We elaborate on certain generalisations and some open problems as well.
Recovering Asymptotics at Infinity of Perturbations of Stratified Media
We consider perturbations of a stratified medium , where the operator studied is . The function is a perturbation of , which is constant for sufficiently large and satisfies some other conditions. Under certain restrictions on the perturbation , we give results on the Fourier integral operator structure of the scattering matrix. Moreover, we show that we can recover the asymptotic expansion at infinity of from knowledge of and the singularities of the scattering matrix at fixed energy....
Recovering the total singularity of a conormal potential from backscattering data
The problem of recovering the singularities of a potential from backscattering data is studied. Let be a smooth precompact domain in which is convex (or normally accessible). Suppose with and conormal to the boundary of and supported inside then if the backscattering data of and are equal up to smoothing, we show that is smooth.
Recursion relations and the asymptotic behavior of the eigenvalues of the laplacian
Regular eigenvalue problem with eigenparameter contained in the equation and the boundary conditions.
Regularity and Decay of Eigenfunctions.
Regularity for a clamped grid equation on a domain with a corner.
Regularity properties of the generalized hamiltonian flow
Relation de Poisson pour l'équation des ondes dans un ouvert non borné. Application au scattering
Relation de Poisson pour l'équation des ondes dans un ouvert non borné
Relative determinants of elliptic operators and scattering theory
Remainder estimates for eigenvalues and kernels of pseudo-differential elliptic systems.