Aarhus University Seal / Aarhus Universitets segl

Regularity of bound states

Jacob Schach Møller
Torsdag, 7 oktober, 2010, at 16:15, in Aud. D3 (1531-215)

We will work through an example of a one-parameter family of rank one perturbations of the Laplacian, with a simple eigenvalue embedded in the continuous spectrum. In particular we will investigate the connection between the regularity of the eigenvalue, as a function of the parameter, and the regularity of the associated eigenfunctions with respect to the generator of dilations.

Finally we see how this example is a borderline case for some general theorems recently established in collaboration with Jeremy Faupin and Erik Skibsted, and for a special case with Matthias Westrich. In particular we rederive and extend an old result of Balslev and Combes on the analytic continuation to a strip of dilated eigenstates.

Kontaktperson: Bent Ørsted