Faddeev eigenfunctions for point potentials in two dimensions

We present explicit formulas for the Faddeev eigenfunctions and related generalized scattering data for point (delta-type) potentials in two dimensions. In particular, we obtain the first explicit examples of such eigenfunctions with contour singularity in spectral parameter at a fixed real energy

Generalized analytic functions, Moutard-type transforms and holomorphic maps

International audienceWe continue the studies of Moutard-type transforms for generalized analytic functions started in our previous paper hal-01222481v1 .In particular, we suggest an interpretation of generalized analytic functions as spinor fields and show that in the framework of this approach Moutard-type transforms for the aforementioned functions commute with holomorphic changes of variables

Moutard transform for the generalized analytic functions

International audienceWe construct a Moutard-type transform for the generalized analytic functions. The first theorems and the first explicit examples in this connection are given

Faddeev eigenfunctions for multipoint potentials

International audienceWe present explicit formulas for the Faddeev eigenfunctions and related generalized scattering data for multipoint potentials in two and three dimensions. For single point potentials in 3D such formulas were obtained in an old unpublished work of L.D. Faddeev. For single point potentials in 2D such formulas were given recently in [P.G. Grinevich, R.G. Novikov, Physics Letters A,376,(2012),1102-1106]

Multipoint scatterers with zero-energy bound states

International audienceWe study multipoint scatterers with zero-energy bound states in three dimensions. We present examples of such scatterers with multiple zero eigenvalue or with strong multipole localization of zero-energy bound states

Moutard transform approach to generalized analytic functions with contour poles

International audienceWe continue studies of Moutard-type transforms for the generalized analytic functions started in hal-01222481v1, hal-01234004v1. In particular, we show that generalized analytic functions with the simplest contour poles can be Moutard transformed to the regular ones, at least, locally. In addition, the later Moutard-type transforms are locally invertible

Faddeev eigenfunctions for multipoint potentials

International audienceWe present explicit formulas for the Faddeev eigenfunctions and related generalized scattering data for multipoint potentials in two and three dimensions. For single point potentials in 3D such formulas were obtained in an old unpublished work of L.D. Faddeev. For single point potentials in 2D such formulas were given recently in [P.G. Grinevich, R.G. Novikov, Physics Letters A,376,(2012),1102-1106]