Scattering theory with two spaces : application to transport equations with obstacles
Let be a finite positive measure on the unit disk and let be an integer. D. Suárez (2015) gave some conditions for a generalized Toeplitz operator to be bounded or compact. We first give a necessary and sufficient condition for to be in the Schatten -class for on the Bergman space , and then give a sufficient condition for to be in the Schatten -class on . We also discuss the generalized Toeplitz operators with general bounded symbols. If and , we define the generalized Toeplitz...
A full description of the membership in the Schatten ideal for 0 < p < ∞ of Toeplitz operators acting on large weighted Bergman spaces is obtained.
We characterize the Schatten class weighted composition operators on Bergman spaces of bounded strongly pseudoconvex domains in terms of the Berezin transform.
We consider the zigzag half-nanotubes (tight-binding approximation) in a uniform magnetic field which is described by the magnetic Schrödinger operator with a periodic potential plus a finitely supported perturbation. We describe all eigenvalues and resonances of this operator, and theirs dependence on the magnetic field. The proof is reduced to the analysis of the periodic Jacobi operators on the half-line with finitely supported perturbations.