We derive a dispersion estimate for one-dimensional perturbed radial Schrödinger operators. We also derive several new estimates for solutions of the underlying differential equation and investigate the behavior of the Jost function near the edge of the continuous spectrum.

Our previous constructions of Borchers triples are extended to massless scattering with nontrivial left and right components. A massless Borchers triple is constructed from a set of left–left, right–right and left–right scattering functions. We find a correspondence between massless left–right scattering S-matrices and massive block diagonal S-matrices. We point out a simple class ...

We consider homogeneous Bose gas in a large cubic box with periodic boundary conditions, at zero temperature. We analyze its excitation spectrum in a certain kind of a mean-field infinite-volume limit. We prove that under appropriate conditions the excitation spectrum has the form predicted by the Bogoliubov approximation. Our result can be viewed as an extension of the result of ...

The paper is devoted to a systematic and unified discussion of various classes of hypergeometric type equations: the hypergeometric equation, the confluent equation, the F 1 equation (equivalent to the Bessel equation), the Gegenbauer equation and the Hermite equation. In particular, recurrence relations of their solutions, their integral representations and discrete symmetries are ...

We present a new rigorous approach based on Orlicz spaces for the description of the statistics of large regular statistical systems, both classical and quantum. The pair of Orlicz spaces we explicitly use are, respectively, built on the exponential function (for the description of regular observables) and on an entropic type function (for the corresponding states). They form a ...

Given an action of a Compact Quantum Group (CQG) on a finite dimensional Hilbert space, we can construct an action on the associated Cuntz algebra. We study the fixed point algebra of this action, using Kirchberg classification results. Under certain conditions, we prove that the fixed point algebra is purely infinite and simple. We further identify it as a C *-algebra, compute its ...

In this article, we want to argue that an appropriate generalization of the Wigner concepts may lead to an asymptotic particle with well-defined mass, although no mass hyperboloid in the energy–momentum spectrum exists.