Scattering Theory with Finite-Gap Backgrounds: Transformation Operators and Characteristic Properties of Scattering Data

Inverse Scattering Theory for One-dimensional Schrödinger Operators with Steplike Finite-gap Potentials

We develop direct and inverse scattering theory for one-dimensional Schrödinger operators with steplike potentials which are asymptotically close to different finite-gap potentials on different half-axes. We give a complete characterization of the scattering data, which allow unique solvability of the inverse scattering problem in the class of perturbations with finite second moment.

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Separable Operators in Scattering Theory

A general theory of non-local, separable operators in scattering theory is developed on the basis of variational techniques and eigenvalue analysis. The formalism gives as limiting cases the three-particle isobar model as well as the quasiparticle formalism. The extreme sensitivity of off-shell multiparticle theories to calculation approximation schemes is minimized by our methods. The theory p...

Time-dependent Scattering Theory for Schrödinger Operators on Scattering Manifolds *

We construct a time-dependent scattering theory for Schrödinger operators on a manifold M with asymptotically conic structure. We use the two-space scattering theory formalism, and a reference operator on a space of the form R×∂M , where ∂M is the boundary of M at infinity. We prove the existence and the completeness of the wave operators, and show that our scattering matrix is equivalent to th...

An analysis of electromagnetic scattering from finite-width strips