Related papers: New formulae for the wave operators for a rank one…
We present here a relation of different types of Friedrichs models and their use in the description and comprehension of resonance phenomena. We first discuss the basic Friedrichs model and obtain its resonance in the case that this is…
We develop direct and inverse scattering theory for Jacobi operators with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give a complete characterization of…
We show that the scattering matrix for a class of Schr\"odinger-type operators with long-range perturbations is a Fourier integral operator with the phase function which is the generating function of the modified classical scattering map.
We continue the study of scattering theory for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In a previous paper we proved the existence of modified wave operators for…
We obtain a formula for the Schwartz kernel of the scattering operator in terms of the Schwartz kernel of the fundamental solution of the wave operator on asymptotically hyperbolic manifolds. If there are no trapped geodesics, this formula…
The Friedrichs operator of a domain (in $\mathbb{C}^n$) is closely related to its Bergman projection and encodes crucial information (geometric, quadrature, potential theoretic etc.) about the domain. We show that the Friedrichs operator of…
We construct wave operators and a scattering operator for the scattering of a charged particle on the Dirac magnetic monopole. The analysis features a two Hilbert space approach in which the identification operator matches states of the…
We prove existence of modified wave operators for one-dimensional Dirac operators whose spectral measures belong to the Szego class on the real line.
We describe the wave functional model for the minimal (symmetric) Sturm-Liouville operator on the finite interval. We construct the wave spectrum of this operator, then, following the abstract scheme, we construct the model space of…
We construct a perturbative framework for understanding the collision of solitons (more precisely, solitary waves) in relativistic scalar field theories. Our perturbative framework is based on the suppression of the space-time interaction…
In the framework of scattering theory, we show how the scattering matrix can be related to the projection on the bound states by an index map of K-theory. Pairings with appropriate cyclic cocyles lead naturally to a topological version of…
In this review paper we carry on our investigations on Schroedinger operators with inverse square potentials on the half-line. Depending on several parameters, such operators possess either a finite number of complex eigenvalues, or an…
The wave equation for spinless particles with the Lorentz violating term is considered. We formulate the third-order in derivatives wave equation leading to the modified dispersion relation. The first-order formalism is considered and the…
In this paper, we develop the radial transfer matrix formalism for unitary one-channel operators. This generalizes previous formalisms for CMV matrices and scattering zippers. We establish an analog of Carmona's formula and deduce criteria…
The Helmholtz wave scattering problem by screens in 2D can be recast into first-kind integral equations which lead to ill-conditioned linear systems after discretization. We introduce two new preconditioners, in the form of square-roots of…
In this work apply the algebra of operators of quantum mechanics in the Helmholtz wave equation in cylindrical coordinates in paraxial approximation to describe the raising and lowering operators for the Laguerre-Gauss modes.
Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…
We continue the study of scattering theory for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In previous papers, we proved the existence of modified wave operators for…
We determine the structure of the spectrum and obtain non-propagation estimates for a class of Toeplitz operators acting on a subset of the lattice $\Z^N$. This class contains the Hamiltonian of the one-dimensional Heisenberg model.
We formulate scattering in one dimension due to the coupled Schr\"{o}dinger equation in terms of the $S$ matrix, the unitarity of which leads to constraints on the scattering amplitudes. Levinson's theorem is seen to have the form $\eta(0)…